Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III

Answers

Answer 1

Given:

[tex]\sin x=-\dfrac{15}{17}[/tex]

x lies in the III quadrant.

To find:

The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others  are negative.

We know that,

[tex]\sin^2 x+\cos^2 x=1[/tex]

[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]

[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]

[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]

x lies in the III quadrant. So,

[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]

[tex]\cos x=-\dfrac{8}{17}[/tex]

Now,

[tex]\sin 2x=2\sin x\cos x[/tex]

[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]

[tex]\sin 2x=-\dfrac{240}{289}[/tex]

We know that,

[tex]\cos 2x=1-2\sin^2x[/tex]

[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]

[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]

[tex]\cos 2x=\dfrac{289-450}{289}[/tex]

[tex]\cos 2x=-\dfrac{161}{289}[/tex]

Using the trigonometric ratios, we get

[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]

[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]

[tex]\tan 2x=\dfrac{240}{161}[/tex]

Hence, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].


Related Questions

PQRS is a parallelogram with PQ=26cm and QR=20cm . If the distance between the longer-sides is 12.5cm , Find​

Answers

Answer:

Below.

Step-by-step explanation:

I am guessing you want the area of the parallelogram.

Take the longer side to be the base.

Area = base * distance between base and opposite side

=  26 * 12.5

= 325 cm^2.

Use this picture to name one pair of ALTERNATE EXTERIOR angles: *

Answers

Answer:

angle 4 is congruent to angle 7

angle 8 is congruent to angle 3

angle 2 is congruent to angle 5

angle 1  is congruent to angle 6

Step-by-step explanation:

alternate exterior angles are congruent, which means identical

London in column bought 1/2 pound of peanuts they are sharing the nuts equally how many pounds of nuts do each person get

Answers

Answer: 1/4 pounds

Step-by-step explanation:

Full question is:

Landon and Colin bought a 1/2 pound of peanuts. They are sharing the nuts equally. How many pounds of peanuts will each person get?​

There are 2 people here - London and Colin - and they are to share 1/2 pounds of nuts equally amongst themselves.

They should therefore divide the nuts in 2:

= Amount of nuts / Number of people

= 1/2 ÷ 2

= 1/2 * 1/2

= 1/4 pounds

Note: When dividing a fraction, multiply the inverse of the divisor.

3/5 = 12/x find the missing numbers in the equivalent ratios

Answers

Answer:

x=20

Step-by-step explanation:

Well just cross multiply if its easier

x(3)=3x

12*5=60

60=3x

x=20

The awnser for this should be 20

If 8 + 4 = 12, then 12 = _ + _

Answers

Answer:

8 + 4

Step-by-step explanation:

It is a fact family.

Answer:

12= 4+8

Step-by-step explanation:

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be.

Answers

Answer:

(1/2,0) is one solution

(-4/3,0) is the other solution.

Step-by-step explanation:

i hope this helps you it might not be right

I don’t. Think I posted this one

Answers

Answer:

The volume of the ice cream cone is 528.1 cubic centimeters.

Step-by-step explanation:

The formula for finding the volume of a cone is V = [tex]\pi r^2\frac{h}{3}[/tex].

Substitute values now:

V = [tex]\pi* 5.8^2*\frac{15}{3}[/tex]

V ≈ 528.1

Please help! I really don't understand...

Answers

it would be 3 feet but i would say i would only agree if it was rounded up to the nearest tenth place

Beth purchased her car for $18,400. Three years later the car was worth $15,200. Find the percent change in the value of her car.​

Answers

Answer:

17.39%.

Step-by-step explanation:

As a percentage (rounded to two decimal places):

A decrease of 17.39%.

Expand and Simplify: (x-5)(x+7)

Answers

distributive property
(x-5)(x+7)
=x^2+7x-5x-35
=x^2+2x-35

Can I get some help?

Answers

Type in the question without g(x)

6. If Aliya can make 10 bracelets in 2 days, how long will it take her to make 35 bracelets? WILL GIVE EXTRA 10 POINTS WILL MARK AS BRAINLIST

a) 175 days
b) 70 days
c) 7 days
d) 5 days​

Answers

Answer:

C

Step-by-step explanation:

Answer:

7 days

Step-by-step explanation:

We need to find bracelets per day.

1 day 2 days

5 bracelets 10 bracelets

since we know how many bracelets she can make per day, all we have to do is divide 35 by 5.

to get 7 days.

Cendrick D'Amitrano works Friday and Saturday delivering pizza. He delivers 8 pizzas on Friday. How many pizzas must he deliver on Saturday to average (mean) 11 pizzas per day?

Answers

Answer:

14

Step-by-step explanation:

there are two days whose mean is 11.for you to get the mean of 11 you had divided by 2

multiply 11 by 2 which is 22

then minus fridays which is 8

I need help on this question plsss help

Answers

Try 28m I hope it’s right

not sure about these either...

Answers

5 is a and 6 is also a

What is the middle value of the following data set? 33, 36, 24 31, 39,44,32

Answers

Mean ( average) = 34.14286
Median (middle ) = 33
Hope that helped or the answer u was looking for

I’ll give u BRANLIEST if u get it right

Answers

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

I think its A plz give me brainliest

Find the value of x.

Answers

x=74°

look at the given picture for stepwise

2/3x - 1/9x + 5 = 20

Answers

Answer:I think the answer is x=27

Step-by-step explanation:

Help please!!! I need it!

Answers

Answer:

1300.62

Step-by-step explanation:

thank me later lolol.

please help ! I’m so confused

Answers

Answer:

2/7 is the scale factor.

Step-by-step explanation:

All you have to do is get two sides that are equal to each other. Let's say Side SR and YX. 3 and 10.5. Do 3/10.5, which is 30/105, which simplified is 6/21, which again simplified is 2/7. So, the scale factor is 2/7.

Plz no links and explain what your doing not just the answer thank you!

Answers

Answer:

I’m confused

Step-by-step explanation:

there is no pic .. :/


Which of the following best describes the shape of the
distribution?
A) skewed to the left
B) bimodal symmetric
C) skewed to the right
D) unimodal symmetric

Answers

Is a) skewed to the left

The shape of the data distribution in the dot plot is: A. skewed to the left.

What is a Left-Skewed Data Distribution?

A data distribution that is left-skew will have the longest tail at your far left, compared to your right.

The dot plot shows similar pattern, therefore, the shape of the data distribution represented by the dot plot is: A. skewed to the left

Learn more about left-skewed data on:

https://brainly.com/question/3252860

#SPJ6

f(7)=
g(7)=
The equation for f(x) is
The equation for g(x) is

Answers

Answer: f(7) = -128

g(7) =  26

Equation of f(x):  f(x)= -11x-51

Equation of g(x): g(x)=3x+5

Step-by-step explanation:

Rate of change of a function: [tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

From the table. Rate of change in f(x)= [tex]\dfrac{f(1)-f(0)}{1-0}=\dfrac{-62+51}{1}=-11[/tex]

Rate of change in g(x)= [tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{8-5}{1}=3[/tex]

Also, the rate of change throughout the function is the same, hence both are linear functions.

Equation of linear function:  [tex]f(x)=mx+c[/tex], where m= rate of change of function, c = f(x) at x=0.

From table, f(0)= -51 , g(0)=5

Equation of f(x): f(x)= -11x-51

Equation of g(x): g(x)=3x+5

f(7) = -11(7)-51 = -77-51 = -128

g(7) = 3(7)+5 = 21+5 = 26

f(7) = -128

g(7) =  26

Can somebody please answer this for me will give
Brainliest

Answers

1.) -2/3
2.) (0, 2)
3.) (0, 3)
I don’t know how to answer 4 and 5 sorry

Paulette wrote the equation below to show f, the amount of framing she needs for a square frame with a side length of s centimeters. f=4s How many centimeters of framing does Paulette need for a square frame that has a side length of 15.3 centimeters. Pls help this is a test A. 61.2 centimeters B. 60.3 centimeters D. 19.3 centimeters C. 11.3 centimeters

Answers

Answer: 61.2 centimeters

Step-by-step explanation:

Since the equation given to show the amount of framing that she needs for a square frame with a side length of s centimeters is:

f = 4s

Therefore, the number of centimeters of framing needed by Paulette for a square frame that has a side length of 15.3 centimeters will be:

f = 4s

f = 4 × 15.3

f = 61.2 centimeters

which sets of three lengths can be used to form a triangle?

A. 7ft, 5ft, 2ft

B. 6ft, 4ft, 8ft

C. 15cm, 18cm

D. 72 in, 10 in, 90 in

E. 6m, 2m, 12m

F. 6 yd, 21 yd, 25yd

Answers

B, F, and the third one I don’t know (I think it’s C)

For C you only listed two lengths. For D and E there is one length that is longer than the other two lengths combined, so it can’t make a triangle. Same thing for A except for A one length is the same as the other two lengths combined.

In October sally drove 560 miles in her car.
the car travelled 34.5 miles for each gallon of petrol used

Petrol cost £1.08 per litre.
1 gallon = 4.55 litres.

Work out the cost of the petrol the car used in October

Answers

The cost is £79.76. Since the car covers 560 miles and 34.5 miles is travelled by one gallon. So, dividing 560 by 34.5 we get 16.23. Since 1 gallon is 4.55 litres, 16.23 gallons is 73.8465. Now the cost of petrol is £1.08 per litre. So, multiplying 73.8465 by £1.08 we have £79.76

The cost of petrol the car used in October is;

Amount spent on fuel in October = £79.76

Distance sally drove in October = 560 miles

She used 1 gallon of petrol for every 34.5 miles she drove.

Thus, number of gallons of petrol she used for the month of October on the car = 560/34.5 gallons

Now, we are told that;

1 gallon = 4.55 litres

Thus; 560/34.5 gallons = (560/34.5) × 4.55/1

Quantity of petrol she used for the month in liters = 73.855 litres

Petrol costs £1.08 per liter.

Thus;

Amount spent on fuel in October = 1.08 × 73.855

Amount spent on fuel in October = £79.7634 ≈ £79.76

Read more at; https://brainly.com/question/22940138

Cendrick D'Amitrano works Friday and Saturday delivering pizza. He delivers 8 pizzas on Friday. How many pizzas must he deliver on Saturday to average (mean) 11 pizzas per day?

Answers

Answer:

Number of pizza deliver on Saturday = 14 pizza

Step-by-step explanation:

Given:

Number of delivery day (Friday, Saturday) = 2

Number of pizza deliver on Friday = 8

Average of delivery (Mean) = 11 pizza

Find:

Number of pizza deliver on Saturday

Computation:

Mean = Sum of pizza / Number of delivery day

11 = [8 + Number of pizza deliver on Saturday] / 2

22 = 8 + Number of pizza deliver on Saturday

Number of pizza deliver on Saturday = 22 - 8

Number of pizza deliver on Saturday = 14 pizza

Describe the error in the work shown.

Answers

Answer:

where is the question

Step-by-step explanation:

Where is the question?
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