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

√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

m

step-by-step explanation:

step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.