Algebra 2 help!

Question

cosθ-tanθcosθ=0

a)0, π/4,4,5π/4

b)π/4,3π/4,5π/4,7π/4

c)π/2, 3π/4, 3π/2, 7π/4

d)π/2,7π/6, 3π/2, 11π/6

Answer 1

I assume they are asking for the angles that satisfy the equation.....

FIRST, simplify the equation:

tanΘ * cosΘ = sinΘ (see note 1 below)

So the equation becomes:

cosΘ - sinΘ = 0

or:

cosΘ = sinΘ

The cos and sin of an angle are equal at angles of 45 deg + N(90)----eg 45, 135, 225....etc.

In radian measure, this is:

π/4 + N (π/2)----eg π/4, 3π/4, 5π/4....etc.