If sin theta 45 and theta is in QII find cos theta tan the

If sin theta = 4/5 and theta is in QII, find cos theta & tan theta. Verify the identity: 1 - sin^2 x/cos x = cos x Verify the identity: cos^2x tan^2x + cos^2x = 1 Solve (sin x + 1)(tan x - 1) = 0 in the interval [0, 2 pi) Solve 4cos^2 x = 1 in the interval [0, 2 pi). Find the exact value of sin(60 degree + 45 degree). Find the exact value of cos(285 degree) Given sin theta = -3/5, theta in Q4. Find sin theta cos theta Solve right triangle ABC if a = 5 and c = 10

Solution

1. sin theta=4/5

theta is in second quadrant

here opposite=4    and    hypotenuse=5

Adjacent=sqrt(25-16) =3

Cos theta=adjacent/hypotenuse

cos theta=-3/5

tan theta=sin theta/cos theta=-4/3

2. (1-sin²x)/cosx=cos x

Starting with the left side

(1-sin²x)/cosx

cos²x/cosx=cosx

3. tan²x cos²x +cos²x=1

Starting with the left side

cos²x(tan²x +1)

cos²x*sec²x

cos²x(1/cos²x)=1