Use the given information to find the exact value of sin 20

Use the given information to find the exact value of sin 20, cos 20, and tan 20. cos theta = 20/29 theta lies quadrant IV sin 2theta = cos 2 theta tan 2 theta = (Type an integer or a fraction. Simplify your answer.)

Solution

given cos =20/29

then sin^2 + cos^2 =1

sin^2 = 1 - (20/29)^2

sin^2 = 1 - 400 / 841

sin^2 = 441 /841

sin = -21/29 (since theta is in IV quadrant)

a).

Sin2 = 2sin cos

= 2 * -21/29 * 20/29

= -840/841

b). Cos2 = 2cos^2 - 1

= 2(400/841) - 1

= -41 / 841

c). tan2 = sin2 / cos2

= 840 / 41