Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,400 questions

17,804 answers

1,438 comments

39,756 users

Use the information given about the angle θ, 0 ≤ θ < 2π, to find the exact value of

0 votes
Use the information given about the angle θ, 0 ≤ θ < 2π, to find the exact value of

(a) sin (2θ)                   (b) cos (2θ)                              (c) sin (θ/2)                                  (d) cos (θ/2)

sin θ = 3/5,              0 < θ < π/2
asked Jan 27, 2015 in PRECALCULUS by anonymous

2 Answers

0 votes

Step 1:

The trigonometric function is image in the interval image.

image.

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

image

image.

Where image lies in quadrant I.

In quadrant I, the six trigonometric functions are positive.

image.

Step 2:

(a)

Find image.

Use double-angle formula : image.

image

Substitute image and image in above expression.

image

image.

Step 3:

(b)

Find image.

Use double-angle formula : image.

image

Substitute image and image in above expression.

image

image.

answered Jan 27, 2015 by joseph Apprentice
0 votes

Contd....

Step 4:

(c)

Find image.

Use half-angle formula : image.

image

Substitute image in above expression.

image

Where image lies in quadrant I, since image lies in quadrant I.

image.

Step 5:

(d)

Find image.

Use half-angle formula : image.

image

Substitute image in above expression.

image

Where image lies in quadrant I, since image lies in quadrant I.

image.

Solution :

(a) image.

(b) image.

(c) image.

(d) image.

answered Jan 27, 2015 by joseph Apprentice

Related questions

...