The terminal side of θ in standard position contains the point (3, 0). Find the exact values of the six trigonometric functions of θ

Answers

Answer 1

[tex]\textit{we know that }\theta \textit{ contains the point }(\stackrel{x}{3}~~,~~\stackrel{y}{0})\textit{, let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ r^2=a^2+b^2\implies r=\sqrt{a^2+b^2}\implies r=\sqrt{3^2+0^2} \qquad \begin{cases} r=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ r=\sqrt{3^2}\implies r=3[/tex]

[tex]\rule{34em}{0.25pt}\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} =\cfrac{y}{r}\implies \cfrac{0}{3}\implies 0 \\\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse} =\cfrac{x}{r}\implies \cfrac{3}{3}\implies 1 \\\\\\ tan(\theta)=\cfrac{opposite}{adjacent} =\cfrac{y}{x}\implies \cfrac{0}{3}\implies 0[/tex]

[tex]cot(\theta)=\cfrac{adjacent}{opposite} =\cfrac{x}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ csc(\theta)=\cfrac{hypotenuse}{opposite} =\cfrac{r}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ sec(\theta)=\cfrac{hypotenuse}{adjacent} =\cfrac{r}{x}\implies \cfrac{3}{3}\implies 1[/tex]


Related Questions

How do I do this ? no links please

Answers

Ask your teacher. It’s the best help you can get because this doesn’t make any sense. To get your teachers help a quick email would do

Hey there!


ASSUMING….
-14.4 = -1.2m

-1.2m = -14.4

DIVIDE -1.2 to BOTH SIDES

-1.2m/-1.2 = -14.4/-1.2

SIMPLIFY IT!

m = -14.4/-1.2

m = 12


Therefore, the answer should be:

m = 12


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Please help me quick…


Answers

20- +3

21- -7

22- +4

23- 8

24- 4

ask your teacher for further guidance because explaining negatives is difficult for me

Answer:

20) - 2+5

= 3

21) 8+(-15)

=8 - 15

= - 7

22) - 10 +14

= 4

23) 6-(-2)

=6 +2

= 8

24) - 16-(-20)

= - 16 +20

= 4

Step-by-step explanation:

This is step by step explanation

Please Mark me brainlist


Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answers

Answer:

70

Step-by-step explanation:

the figure shown is a parallelogram with a base length of 10 ft and a height of 7 ft

the area of a parallelogram can simply be calculated by multiplying the base length by the height

hence, area = 7 * 10 = 70

Answer: 10 times 7

Step-by-step explanation: 10 times 7

Work out the size of angle X ?

Answers

Answer:

x = 121°

Step-by-step explanation:

∠ 1 + 115° = 180°

∠ 1 = 180 - 115

∠ 1 = 65°

∠ 2 + 304° = 360°

∠2 = 360 - 304

∠ 2 = 56°

∠ 1 + ∠ 2 + ∠ 3 = 180°

65° + 56 ° + ∠ 3 = 180°

∠3 = 180 - 65 - 56

∠ 3 = 59°

∠3 + x = 180°

59° + x = 180°

x = 180 - 59

x =  121 °

can someone help me with this problem!

Answers

C. -1

Hope this helps! :)

______________

Answer:

-1

Step-by-step explanation:

Simplify the real and imaginary parts of the expression. That’s probably as simple as i can get it.

Hope this helps! :)

Ms. Cortez was building doll houses to sell at a toy store. She had to spend $184 on tools before she could begin to work. Each doll house cast $17 to make. She planned to sell the doll houses for $29 each. How many doll houses did she need to sell to make a profit?

Answers

Answer:

A minimum of 16 dollhouses

Step-by-step explanation:

profit on each dollhouse= sp-cp= 29-17= $12

if we divide 184 by 12 we get abt 15.33, which means, she has to sell more than 15 Dollhouses to make a profit.

so the minimum number of dollhouses to be sold are 16

A caterer charges a setup fee of $50, plus $20 per person How much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 discount off the total?

Answers

They will charge $165 for each person
The answer is 650

20x35= 700

700+50 = 750

750-100= 650

i need help with this plz

Answers

Answer:

-4 is the correct answer

Answer:

y=18

Step-by-step explanation:

equation:y=3x -7

x=7 then y =?

substitute the vale of x in the equation

y=3x-7

y=3*7-7

y=21-7

y=18

therefore the value of y corresponds to 7 is 18.

Please help find volume of cone

Answers

Answer:

5275.2 m³

Step-by-step explanation:

We need the radius first:

[tex]\sqrt{l^2- h^2}[/tex] = 12

Formula for volume = πr²*h/3

Volume = 3.14 * 144 * 35/3

Volume = 5275.2

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

What do you get when you subtract-3xy from 5xy

Answers

Answer:

8xy

Step-by-step explanation:

(5xy)-(-3xy)= 5xy+3xy=8xy

Why:

Well if you have 5 of that something and get 3 more of that something you have 8 of that something.

Answer:

8xy

Step-by-step explanation:

5xy--3xy

a - and a - equal a +, so it's 5xy+3xy, which equels 8xy.

A runs 25% faster than B and is able to give him a start of 7 metres to end a race in dead heat. What is the length of race?

Answers

Answer:

35 metres

Step-by-step explanation:

The question states that A runs 25% faster than B. This means that, for every 1 second that B runs, A runs 1.25 second

Assuming that the total length of the race, that we're looking for, is D. Then we can say that B made a total distance of D-7 meters, and A runs D.

time taken by A = [tex]\frac{D}{1.25}[/tex]

time taken by B = [tex]\frac{D-7}{1}[/tex]

equating both together, we have

[tex]\frac{D}{1.25}[/tex] = [tex]\frac{D-7}{1}[/tex]

1.25D  - 8.75 = D

1.25D - D = 8.75

0.25D = 8.75

D = 8.75/0.25

D = 35

On the number line below, length
AB = [?]
A
В
16
45

Answers

Answer:

29

Step-by-step explanation:

45 - 16 =

Calculate the area of triangle ABC with altitude CD, given A (−3, −4), B (−6, 2), C (0, 0), and D (−4, −2). (5 points)

Question 8 options:

1)

14 square units

2)

15 square units

3)

18 square units

4)

20 square units

Answers

Answer: 2) 15 square units

Step-by-step explanation:

The area of the triangle is 15 square units if the triangle ABC with altitude CD, given A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2) which is correct option (2)

What is the distance between two points?

The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

Given that a triangle ABC with altitude CD.

The coordinates for the triangle are A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2)

Given that the distance between C and D will be the height of the triangle

Since, the distance between the points by using the distance formula:

= √ (x₂ – x₁)² + (y₂ – y₁) ².

height = √ (-4 – 0)² + (-2 – 0) ²

height = √20

base = √45

Area of triangle = (1/2)base x height

Area of triangle = (1/2)√20×√45

Area of triangle = (1/2)30

Area of triangle = 15 square units

Hence, the area of the triangle is 15 square units if the triangle ABC with altitude CD

Learn more about distance between two points here:

https://brainly.com/question/15958176

#SPJ2

Round 187.890 to the nearest 10 000

Answers

Answer:

190,000

190,000

190,000

Step-by-step explanation:

190,000

190,000

What is 16.99 times 0.80

Answers

Answer:

Hi, there your answer is 13.592

Step-by-step explanation:

Find m 22 in the figure below.
95°
2
72°

Answers

Answer:

<2= 23°

Step-by-step explanation:

180°- 95°= 85°

(95° is on a straight line, angles on a straight line adds up to 180° so 95° is being subtracted from 180°. Therefore the next angle in the triangle will be 85°)

To find <2

180- (85°+ 72°)

(Angles on a triangle adds up to 180°)

180- 157

= 23

WILL GIVE BRAINLIST


WRITE THE PHRASE AS A VARIABLE EXPRESSION. USE X TO REPRESENT “a number”



THE PRODUCT OF 4 AND A NUMBER

Answers

Answer:

x+14.  

Sum of a number and 14 is x+14.

 

Find the range for the following list of values:
1, 2, 4, 7

Answers

1-7 so 6 is your range i think!

Answer:

below

Step-by-step explanation:

Rage =

highest value - lowest value

= 7 - 1

=6

Recall what you know about similarity. If circle B is similar to circle A, what must exist?

Answers

The similarities of two circles is dependent on the radius of circle A and circle B. So the radius of both circles must exist for the circles to be similar.

Given that:

Circles A and B

To prove the similarities of the two circles, the radius of both circles must be known.

Assume the radius of circle A is [tex]r_A[/tex] and the radius of circle B is [tex]r_B[/tex].

The similarity of both circles is proved using:

[tex]r_A = k * r_B[/tex]

or

[tex]r_B = k * r_A[/tex]

where k represents the scale of dilation

Hence, the radius of both circles must exist for the circles to be similar.

Read more about circle similarities at:

https://brainly.com/question/403891

If a1 = 6 and an = 3 + 2(an-1), then a2 equals

no links

Answers

Answer:

15

Step-by-step explanation:

Given that a1 = 6

an =  3 + 2(an-1),

Substitute n = 2 into the formula

a2 = 3 + 2(a1)

a2 = 3 + 2(6)

a2 = 3+12

a2 = 15

Hence the second term of the sequence is 15

Solve this equation

2 . B - 19 = -11

Answers

Answer:

B=8

Step-by-step explanation:

you add 19 to both sides of the equation to get B by itself.

[tex]B=-11+19\\B=8[/tex]

answer:

8,

reason

11+8=19

alalalalalalalaalalalalal

20character minimum^

Find the solution(s) to the system of equations represented in the graph.

A. (0, 3) and (3, 0)
B. (0, 3) and (−3, 0)
C. (0, −3) and (3, 0)
D. (0, −3) and (−3, 0)

Answers

Answer:

(-3,0) and (0,3)

Step-by-step explanation:

The solution to the system of equation is where the two graphs intersect

The intersect at two points

(-3,0) and (0,3)

Can someone help me? It's urgent and thank you!
Put either A,B,C,D,E in r= and also put A,B,C,D,E in the find the 6th term put whatever your answer's lead you too

Answers

number a is too low so we will work with c after all I put that and got it eight

Your answer is C. - 972

I found 3 by dividing 36 by 12. I hope the image is self- explanatory.

What is the equation for a parabola if the vertex is at (5,4) and goes through the point (3,-8)

Answers

Answer:

[tex]y=-3(x-5)^2+4[/tex]

Step-by-step explanation:

Hi there!

Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:

[tex]y=a(x-h)^2+k[/tex] where the vertex is located at [tex](h,k)[/tex] and a is a numerical value

1) Plug the vertex into the equation

[tex]y=a(x-h)^2+k[/tex]

Plug in the vertex (5,4)

[tex]y=a(x-5)^2+4[/tex]

2) Solve for a

[tex]y=a(x-5)^2+4[/tex]

Plug in the given point (3,-8) and solve for a

[tex]-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4[/tex]

Subtract 4 from both sides

[tex]-8-4=4a+4-4\\-12=4a[/tex]

Divide both sides by 4

[tex]\frac{-12}{4} = \frac{4a}{4} \\-3=a[/tex]

Therefore, a=-3. Plug this back into [tex]y=a(x-5)^2+4[/tex]:

[tex]y=-3(x-5)^2+4[/tex]

I hope this helps!

Select all of the following that are equivalent to 1 10,000 1 A. (10,000) B.(-10,000 D c. 100) ( O D. (10)​

Answers

Answer:

A. 10,000

Step-by-step explanation:

A. is 10,000, so it is equivalent to 10,000

B. -10,000    No

C. 100   No.

D. 10   No.

Round to the nearest cent or whole number as needed. How many males had fatal car accidents last year if there were 1761 fatal car accidents and about 42% of the fatalities were male?

Answers

Answer:

740

Step-by-step explanation:

42% of 1761 = 0.42 * 1761 = 739.62

Answer: 740

Box A has 14 black pens and 6 blue pens box B has 9 black pens and 3 blue pens a pen is randomly chosen from each box list these events from least likely to most likely

Answers

Answer:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

Black - Black

Black - Blue

Blue - Black

Blue - Blue

Probability of each outcome:

Black-Black:

14 out of 20, and then 9 out of 12. So

[tex]P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}[/tex]

Black-Blue:

14 out of 20, then 3 out of 12. So

[tex]P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}[/tex]

Less likely than black-black.

Blue - Black:

6 out of 20, then 9 out of 12. SO

[tex]P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}[/tex]

More likely than black-blue, less likely than black-black.

Blue - Blue

6 out of 20, then 3 out of 12

[tex]P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}[/tex]

Least likely of the outcomes.

List these events from least likely to most likely:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

what is the average rate of change from x equals negative 1 to x equals 1​

Answers

Answer:

This question is incomplete, so I can not give you an exact answer, but I can give you the answer for the general case.

If we have a function f(x), the average rate of change between the values:

x = a and x = b,

is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

So if we want to find the rate of change from:

x = -1 to x = 1

it is just:

[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{f(1) - f(-1)}{2}[/tex]

So just to show an example, if:

f(x) = 3*x^2 - 5

the average rate of change in that interval will be:

[tex]r = \frac{f(1) - f(-1)}{2} = \frac{3*1^2 - 5 - (3*(-1)^2 - 5)}{2} = \frac{-2 - (-2)}{2} = 0[/tex]

What is the surface area of the cylinder with height 4 yd and radius 7 yd? Round your answer to the nearest thousandth.

Answers

Answer:

483.87yd^2

Step-by-step explanation:

Given data

Height= 4yd

Radius= 7yd

The expression for the surface area of a cylinder is given as

Surface area=  2πr (4+ 7)

Surface area= 2*π*7 (4 + 7)

Surface area = 14π (11)

Surface area= 154*3.142

Surface area= 483.87yd^2

Hence the surface area is 483.87yd^2

Sierra says that she can simplify the side of the inequality shown by combining the terms within the parentheses but that she​ can't do the same thing on the side. Is Sierra​ correct? Explain.

Answers

Answer:

Yes, Sierra is correct

Step-by-step explanation:

Given

[tex]4(y + 7) > -3 (4 + 5)[/tex]

Required

Is she correct

The right parenthesis has 4 + 5.

This can be simplified as: [tex]4 + 5 = 9[/tex]

So, we have:

[tex]4(y + 7) > -3 (4 + 5)[/tex]

[tex]4(y + 7) > -3 *9[/tex]

The left parenthesis has y + 7.

This cannot be simplified because y is a variable and 7 is a number.

Hence, Sierra is correct.

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DON'T UNDERSTAND SOMEONE CAN YOU HELP PLEASEMY TEACHER IS ANNOYING ME TO DO THIS SUM simplify 22+[55-{72(7+52-11)+3}+2] 1) what parts of a person's life do you believe the government SHOULD have control over in Canada?2) what parts of a person's life do you believe the government SHOULD NOT have control over in canada?i rly need someone help asap, thanks in advance! Need help ASAP DUE SOON PLEASE AND SHOW WORK ?!!! PLEASE HELP!! Best answer gets brainliest.Read the following passage from Muir's "Calypso Borealis" and answer the question.Oftentimes I had to sleep without blankets, and sometimes without supper, but usually I had no great difficulty in finding a loaf of bread here and there at the houses of the farmer settlers in the widely scattered clearings. With one of these large backwoods loaves I was able to wander many a long wild fertile mile in the forests and bogs, free as the winds, gathering plants Identify and explain the tone of this passage. What specific words contribute to the tone? Then, explain how the tone of the passage would change if the words "travel" and "lonely as the solitary cloud, collecting and numbering plants" replaced the bolded words. Be sure to identify the new tone and explain how the changed words create that tone. Your response should be a paragraph of 35 sentences.(no links pls) The Necessary and Proper Clause is significant because it gives congress: The following passage has not been edited. There is and error in in each line of the the passage given below. Identify the error and write the incorrect word and the correction in your answer sheet against the correct blank number.Incorrect correctDecide to make his followers laughPeople flock to him to listenTo his jokes and return home laughingThe Monk will make fun of himselfHe make sure that there, inThe crowd, were not a single gloomy face. His last wish is that heWould be cremated under a treeIn his compoundplease answer this I will mark u as brainlist draw any two microbes 8) what is the side ratio?. 9) what is the perimeter of RST? A boy was playing softball in a neighborhood park when a ball was hit over the fence and into a neighbor's yard. The boy knocked on the neighbor's door and obtained permission from her to retrieve the ball from her yard. As he bent to retrieve the ball in some bushes, the boy brushed against an exposed electric wire that was partially hidden by the bushes and received a severe electric shock and burns. The neighbor had failed to maintain the bushes, allowing them to become overgrown, and was not aware of the exposed wire. If the boy sues the neighbor in a jurisdiction that applies the traditional rules for landowners and possessors of land, what is the likely result use the protractor to find the measure of each angle:a. CABb. FABc. EABd. HAF which constitutional principle served as inspiration for the creation of the three branches of us federal government? Graph inequality y< -3/2x -6 i have absolutely no idea what this answer is i worked on it for 15 minutes could i get some help please Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500 pumpkins in herharvest. She takes a random sample of 11 of these pumpkins and finds they have a mean weight of 44 kg and astandard deviation of 6.7 kg. The weights in the sample were roughly symmetric with no outliers. The NIMS Management Characteristic of Chain of Command and Unity of Command means that each person: In which way did Bradstreet differ from other Puritan women? In an energy pyramid, up to 10% of energy is transferred between trophic levels. Suppose the producer level has 50,000 J. Approximately how much energy is available to the next level, the primary consumer, in this energy pyramid? Need in hurry important please The area of a circle is 3.14 square millimeters . What is the circle's radius ?