Question

Given tan θ = 2 and sin θ < 0. Find cos(θ +pi/4)

Answer 1

Answer:

√10 / 10

Step-by-step explanation:

tan θ > 0 and sin θ < 0, so θ is in quadrant III.  That means cos θ < 0.

cos(θ + π/4)

Use angle sum formula.

cos θ cos(π/4) − sin θ sin(π/4)

½√2 cos θ − ½√2 sin θ

Factor.

½√2 cos θ (1 − tan θ)

½√2 cos θ (1 − 2)

-½√2 cos θ

Write in terms of secant.

-½√2 / sec θ

Use Pythagorean identity (remember that cos θ < 0).

-½√2 / -√(1 + tan²θ)

-½√2 / -√(1 + 2²)

½√2 / √5

√10 / 10