Trig Precalculus Help

Question

If sin θ = 0.25, find the value of sin(−θ).

If cos θ = 2 3 , find the value of cos(θ + π).

How do I solve this?

Answer 1

Looking at the graph of y = sin(x), you can see that it is an odd function. That means f(θ) = -f(θ) so if sin(θ) = 0.25, then sin(-θ) = -0.25

There's some sort of typo in the second part of your question because the cos(θ) is never 23. Perhaps you meant to say cos(θ) = 0.23. Since y = cos(θ) is cyclical, repeating every 2π, then cos(θ) = cos(θ + 2π) and cos(θ + π) will be a negative of those values (halfway around the unit circle.