One of sin x, cos x, and tan x, are given. Find the other two if x lies in the specifed interval.

Question

Tan x = 1/2

X ∈ ( π , 3π/2 )

Answer 1

Angle is in the third quadrant between π and 3π/2.

The hypotenuse, H, is:

H = √(1² + 2²)

H = √5

sin(x) = -1/√5 (3rd quadrant, sine < 0)

sin(x) = -√5/5

cos(x) = -2/√5 (3rd quadrant, cosine < 0)

cos(x) = -2√5/5

Answer 2

Answer 3