determine tan(t) if cos(t) = -12/13 and sin(t)
Answers
Determine tan(t) if cos(t) = -12/13 and sin(t) = 5/13
Answer:tan(t) = [tex]\frac{-5}{12}[/tex]
Step-by-step explanation:Method 1:
The sketch of the trigonometry is attached to this response.
Since cos(t) is negative and sin(t) is positive, then t should be in the second quadrant as shown in the sketch. A triangle is formed.
We know that, in a given triangle, the cosine of a given angle is the ratio of the adjacent side to the hypotenuse side.
i.e
cos (t) = adjacent / hypotenuse = - 12 / 13
Where;
adjacent = -12 [the adjacent side is in the -x direction]
hypotenuse = 13
Also, the sine of a given angle is the ratio of the opposite side to the hypotenuse side.
sin (t) = opposite / hypotenuse
Where;
opposite = 5
hypotenuse = 13
These sides - opposite, adjacent and hypotenuse - are labelled in the sketch.
From this triangle and the labels, the tangent can be found.
We know that the tangent of a given angle is the ratio of the opposite side to the hypotenuse side. i.e
tan (t) = opposite / adjacent
Where;
opposite = 5
adjacent = -12
Therefore,
tan (t) = [tex]\frac{-5}{12}[/tex]
Method 2:
The tangent of an angle is the ratio of the sine of that angle to the cosine of that angle. i.e
tan(t) = sin(t) / cos (t) ---------------(i)
sin(t) = 5 / 13
cos(t) = -12 / 13
Substitute for sin(t) and cos (t) in equation (i)
tan(t) = [5 / 13] / [-12 / 13]
tan(t) = [5 / 13] x [-13 / 12]
tan(t) = [tex]\frac{5}{13} * \frac{-13}{12}[/tex]
tan(t) = [tex]\frac{-5}{12}[/tex]
Related Questions
Question 5 of 30
What is the period of the graph of y
5cos(4x – 1) + 3?
Answers
Answer:
Period is [tex]\frac{\pi}{2}[/tex]
Step-by-step explanation:
For the function [tex]y=acos(bx-c)+d[/tex], the period is [tex]\frac{2\pi}{|b|}[/tex].
Therefore, the period of the function is [tex]\frac{2\pi}{|b|}=\frac{2\pi}{|4|}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex].
What this means is that the function's wave cycle will repeat every [tex]\frac{\pi}{2}[/tex] units.
Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500 pumpkins in her
harvest. She takes a random sample of 11 of these pumpkins and finds they have a mean weight of 44 kg and a
standard deviation of 6.7 kg. The weights in the sample were roughly symmetric with no outliers.
Answers
Answer:
44+-3.169(6.7/root11)
Step-by-step explanation:
The 99% confidence interval for the mean weight in kg of pumpkins grown by Fiona in the harvest for the provided sample is,
[tex]44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
What is mean and standard deviation?The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500 pumpkins in her harvest.
She takes a random sample of 11 of these pumpkins. Here, the sample size is 11 which is less than 30. Thus, use the formula mentioned below.
[tex]\overline x\pm t\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Here, (n) is the sample size, [tex]\overline x[/tex] is the mean of the sample.
Degree of freedom is,
[tex]DF=11-1=10[/tex]
For this, the value of t from the t table is 3.169 for 99% confidence interval.
The mean weight of 44 kg and a standard deviation of 6.7 kg they find. Put these values in the above formula,
[tex]\overline x\pm t\times\dfrac{\sigma}{\sqrt{n}}=44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
Thus, the 99% confidence interval for the mean weight in kg of pumpkins in the harvest for the provided sample is,
[tex]44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
Learn more about the mean here;
https://brainly.com/question/14532771
What is the x-intercept of the line shown below? Enter your answer as a coordinate pair.
Answers
Answer:
(1,0)
Step-by-step explanation:
The area of a circle is 3.14 square millimeters . What is the circle's radius ?
Answers
Answer:
Step-by-step explanation:Circle
Solve for radius
r≈1
A Area
3.14
d
r
r
r
d
d
C
A
Using the formula
A=
π
r
2
Solving forr
r=
A
π
=
3.14
π
≈
0.99975
Answer:
Radius of circle is 1 mm.
Step-by-step explanation:
Area of circle is 3.14 mm ²
Radius of circle
Area of circle = π × ( radius ) ²
substitute the values
3.14 mm² = 3.14 × ( radius )²
divide the values
3.14mm²/ 3.14 = ( radius) ²
1 mm²= ( radius)²
find the square root of 1 mm²
√1mm² = radius
1 mm = radius
Therefore the radius of circle is 1 mm.
At a pet store, Rhonda paid $55 for 8 dog bowls and 6 bones. Kelly paid $32.50 for 2 dog bowls and 9 bones. Determine the cost of one dog bowl (x) and one bone (y). Write a system of linear equations that models this situation.
Answers
Answer:
V = 288π units³
Step-by-step explanation:
The formula for the volume of a sphere is V = (4/3)πr³.
With r = 6 units, the volume of this sphere is V = (4/3)π(6 units)³, or
V = (4π/3)(216 units³), or V = 288π units³
The mean age of 5 people in a room is 33 years. A person enters the room. The mean age is now 33. What is the age of the person who entered the room?
Answers
Answer:
33 years
Step-by-step explanation:
I think you might have made a typo, but it would still be 33 if the mean age stays the same.
What is the slope of a line that is perpendicular to the line y =1/2x+5?
-2
-1/2
1/2
2
Answers
Answer:
[tex] - 2[/tex]
Step-by-step explanation:
Hope it is helpful...
ASAP I HAVE A MATH FINAL PLEASE
Answers
<2 and <6 -----> Neither
<1 and <4 ------> vertical
Hope it helps you...
What is the measure in radians for the central angle of a circle whose radius r = 4 cm, and intercepted arc length s = 1.2 cm? Enter your answer as a decimal in the box. radians
Answers
Answer:
17.1972degrees
Step-by-step explanation:
length of an arc = theta/360 * 2πr
Substitute the given angle;
1.2 = theta/360 * 2(3.14)(4)
1.2 = theta/360 * 25.12
1.2/25.12 = theta/360
0.04777 = theta/360
theta = 360 * .04777
theta = 17.1972
Hence the required angle is 17.1972degrees
CSN someone tell me What 9x6+4=?
Answers
Answer:
58
Step-by-step explanation:
Answer:
9x6+4 = 58
Step-by-step explanation:
9×6 + 4
= 54 + 4
= 58
Ethan invests $3000 in a mutual fund that earns 6% interest per year compounded monthly. After 10 years, the investment is worth $5,458.19. How much interest did he earn?
Answers
Answer:
[tex]A = P(1 +\frac{r}{n} )^{nt}[/tex]
A = 3000(1 + .06/12)^120
strange the question did not want you to calculate the amount
that was given....
the interest is 5,458.19 - 3000 = 2,458.19
Step-by-step explanation:
11. Benjamin plotted -1.5 and 1.6 on a number
line. Which point is further from zero?
12.
Times in 50-meter Dash
Runner
Time (s)
Steve
7.41
Mike
7.38
Daniel
7.43
Mauricio
7.25
Four runners ran the 50-meter dash. The
times are shown in the table above.
Which runner had the fastest time?
Answers
Answer:
11 1.6
12 Mauricio
Step-by-step explanation:
11. Take the absolute value of each number to determine which is furthest from zero
|-1.5| and |1.6|
1.5 and 1.6
1.6 is greater than 1.6 so it is further from 0
12. The fastest time is the smallest time
The ones place all has 7's so look at the tenths place
The smallest number will have the fastest time
Mauricio has a 2 which is the smallest number
Mauricio has the fastest time
Which is the best approximation for the value of 102−−−√?
Answers
Answer:
10
Step-by-step explanation:
it is because when you use a scientific calculator you get 10.09950494
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10
hope this helps
The best approximation for the value of √102 is: 10.
Approximation for √102The square root of 102 is:
√102
=10.09950494
Now if we approximate 10.09950494 it would give us:
Approximation= 10.09950494
Approximation= 10 (Approximately)
Therefore The best approximation for the value of √102 is: 10.
Learn more about approximation here:https://brainly.com/question/1980606
Vasha pays $64.32 for 12 pairs of gloves for the fall. At this rate, how much will she pay for 5 pairs of gloves?
Answers
12 pair=64.32
5 pair=?
first calculate for one pair
one pair= 64.32/12= $5.36
5 pair then would be = $5.36 x 5= $26.8
hope it helps
Answer:
28.6
Step-by-step explanation:
64/12=5.36
5.36x5=28.6
Let me know if I'm wrong.
An art student is mixing blue paint with yellow paint to create a special color. For every 6 gallons of blue paint, they need 4 gallons of yellow paint.
How much yellow paint will they need if they use 30 gallons of blue paint?
Answers
Answer:
The answer is 20 gallons of yellow paint
Answer:
20 gallons of yellow paint.
Step-by-step explanation:
4/6 = x/30 is the equation.
4 represents yellow paint.
6 represents blue paint.
We know 30 gallon of blue paints was used.
But we dont know x , the amount of yellow paint.
Criss cross bottom to top
6× X = 4×30
6x= 120
x=20
The lines represented by the equations y- 6x = -7 and 24y - 4x = 192 are
Answers
Answer:
negative signs
Step-by-step explanation:
Find the measure of angle 1
Answers
Answer:
<1 is 45○
Step-by-step explanation:
180-90 = 90
90 / 2 = 45
Answer:
Each angle=60°
m∠1=180-(60+60)180- (120)=60°--------------------------hope it helps...have a great day!!Find the measure of angle 1
120°
45°
30°
90°
Answers
The answer should be 90 degrees
A 1,260-foot tree has grown at a constant rate each year. In the equation below, t is the age of the tree 28t = 1,260 in years.
Answers
Answer:
45 years
Step-by-step explanation:
28t = 1,260
Divide both sides by 28
t = 45
Let k ( x ) = 2 x + 3 and m ( x ) = 3 x 2 + 7 x − 10 . Find the indicated value. M ( k ( − 4 ) ) =
Answers
Answer: [tex]30[/tex]
Step-by-step explanation:
Given
[tex]k(x)=2x+3[/tex]
[tex]M(x)=3x^2+7x-10[/tex]
[tex]M\left(k(x)\right)[/tex] is given by replacing the [tex]x[/tex] by [tex]k(x)[/tex] from the [tex]M(x)[/tex]
[tex]\Rightarrow M\left(k(x)\right)=3(2x+3)^2+7(2x+3)-10\\\Rightarrow M\left(k(x)\right)=3(4x^2+9+12x)+14x+21-10\\\Rightarrow M\left(k(x)\right)=12x^2+50x+38[/tex]
Now, [tex]M\left(k(-4)\right)[/tex] is
[tex]\Rightarrow M\left(k(-4)\right)=12(-4)^2+50(-4)+38\\\Rightarrow M\left(k(-4)\right)=192-200+38\\\Rightarrow M\left(k(-4)\right)=30[/tex]
Waylon played defense in 12 soccer games. This was 60% of the total number of games he played. How many games did Waylon play?
Answers
Answer:
Waylon played 20 games
Step-by-step explanation:
Have a great summer :)
Answer:
20 games
Step-by-step explanation:
which of the following is an experiment,? A. Rolling a pair die. B.Rolling two pair dice twice. C.Tossing a coin. D.None of these
Answers
Step-by-step explanation:
Hint : we will check for each option whether it is an experiment or not by using the concepts of probability first we will check then if a coin is tossed then it is an experiment or not ? then we will check that if a dice is rolled is it an experiment or not and then we will repeat the same process for choosing a marble from a jar
complete step by step answer and event is a set of outcomes of an experiment to which probability is assigned as take an example when we and I the possibility of 5 appearing on the die is an event if for tossing a coin we do not know the result when a coin is tossed in can give any result whether it will be a head or tails so this is an example for a random experiment if a six-sided dice will be rolled then we do not know what is about to come there result can be anything from 126 so it is also an example for random experiment choosing a marble from a jar is also an experiment because we are choosing one marble from the jar and experiment is a work in which a result can be anything hence option d is the correct option not probability is how likely something is about to happen when a coin is tossed there are two possibility outcomes heads or tails show the probability of an outcome 1
( number of ways it can happen )÷
( total number of outcomes)
so when a coin is tossed the total number of outcomes are to solve the probability of a current head is 1/2
I need help solving these
Answers
Jacob cuts 4 meters of a ribbon into 3 pieces, the length of the first piece is 1.28 meters.The length of the second one is 1.65 meters. Work out the length of the 3rd piece.
Answers
Answer:
1.07meters
Step-by-step explanation:
Given data
Lenght of ribbon= 4 meters
Number of pieces= 3 pieces
Length of first piece= 1.28meters
Length of second piece= 1.65meters
Let the length of the third piece be x meters
Hence
1.28+1.65+x= 4
2.93+x=4
x= 4-2.93
x=1.07meters
Hence, the length of the third piece is 1.07meters
One of the angles of a parallelograrn is equal to 40°. Find the rest of the angles.
NEED IT QUICK WILL MARK BRAINLIEST 20 POINTS
Answers
Answer:
Angles ⇒ 40°, 40°, 140°, 140°
Step-by-step explanation:
Since the opposite angles of a parallelogram are equal, and the angles in a quadrilateral add up to 360°:
360 - 2(40) = 280
280/2 = 140°
Angles ⇒ 40°, 40°, 140°, 140°
The perpendicular of a right angled triangle measures 3m, the area of the triangle 6 sq. m. What are the lengths of the other two sides of the triangle?
Answers
Answer:
the length of the other sides are
4 m and 5 m
Step-by-step explanation:
the area of right triangle = ½× b x h = 6
let b = 3m => h= 2×6/ 3 = 4m
and the hypotenuse = √3²+4²=√25= 5m
Answer:
5m and 4m
Step-by-step explanation:
(area of a right angle triangle)=1/2×b×h
let b = 3m
1/2×6×2=6×2=12/3=4m
and it's hypotenuse= 3
[tex]3 { }^{2} + 4 {}^{2} = \sqrt{25 {}^{2} } [/tex]
= 5m
An aquarium store recommends that the minimum size for a goldfish tank is 5.8 gallons plus an additional 0.6 gallon for each
fish that is added to the tank. Which expression represents the minimum number of gallons needed in a tank for x fish?
Answers
Answer: 5.8 +0.6x
Step-by-step explanation:
Given: f(x) = 2x4 +10 and g(x) = 4x – 15 What is the value of g f (x)?
Answers
Step-by-step explanation:
g (f(x)) = 4(2x⁴+10)-15
= 8x⁴+40-15
= 8x⁴+25
HELP NEEDED NOW !!!! PLEASE
Select all statements that are true. Be prepared to explain your reasoning.
1. 4-2(3+7)=4-2•3-2•7
2. 4-2(3+7)=4+-2•3+-2•7
3. 4-2(3+7)=4-2•3+2•7
4. 4-2(3+7)= 4-(2•3+2•7)
Answers
Answer:
1, 2, and 4 are true statements.
Step-by-step explanation:
1. The positive symbols will become negative once you removed the parenthese. For instance, 2-(3+2)=2-3-2. It’s the same in this problem. 4-2(3+7)=4-(2•3+2•7)=4-2•3-2•7
2. Distributive property. 4-2(3+7)=4+[-2(3+7)]=4+(-2•3+-2•7)
3 is false because the positive symbol is not changed into negative symbol after the parentheses were removed.
4. 4-2(3+7)=4-[2(3+7)]=4-(2•3+2•7)
Find the nth term of the following sequence 5,20,45,80,125
Answers
Answer:
{5, 20, 45, 80, 125} = 5{1, 4, 9, 16, 25} = 5{1², 2², 3², 4², 5²}
→ U{n} = 5n²
Step-by-step explanation: