Question

If tan θ=1/4 and cos θ≤0, find the exact value of sin x

If you can answer this soon that would be great.

Answer 1

Explanation:

Tan(theta) = Sin(theta) / cos(theta)

1/4 = sin(theta) / sqrt(1 - sin^2(theta) ) Cross multiply

sqrt(1 - sin^2(theta)) = 4*sin^2(theta) Square both sides.

1 - sin^2(theta) = 16 * sin^4 (theta) Transfer the left side to the right side.

0 = 16 sin^4(theta) + sin^2(theta) - 1

Use the quadratic formula to find a value for sin^2(theta)

a = 16

b = 1

c = - 1

I'll leave solving the quadratic to you.

There are two answers

sin^2(theta)= .22069

The other root is - 0.28 which you cannot use.

Sin(theta) = +/- 0.4698

Cos(theta) is < 0 in quads 2 and 3

So sin(theta) is positive in quad 2

and sin(theta) is minus in quad 3