What is the expression as a function of 0?

Question

Answer 1

I'm not sure if you typed 0 in your question because you didn't know how to type θ, or if you confused the symbol for the constant number 0 for symbol for the variable θ. If so, one source of your confusion may be that you read θ (the greek letter theta) as 0 (the number zero). Otherwise, to solve this problem you will have to use a trig identity.

A good way to get yourself unstuck on any problem involving trig functions is to look up a list of trig identities, and then search for an identity that you can apply to your problem.

In this instance, since we have cos(150° - θ), we should use one of the sum and difference identities, namely cos(α - β) = cos(α) cos(β) + sin(α) sin(β). Then, we let α = 150° and β = θ, so we get

cos(150° - θ) = cos(150°) cos(θ) + sin(150°) sin(θ).

Using the unit circle, we know that cos(150°) = - √3/2 and sin(150°) = 1/2, so we can eliminate the angle measures via substitution and obtain:

cos(150° - θ) = -√3/2 cos(θ) + 1/2 sin(θ).

Now try this with another problem to solidify your understanding!