Question

f(θ)=sin(θ),g(θ)=cos(θ). find the exact value of the function -g(-θ) if θ = 45°. do not use a calculator
select the correct choice below and fill in any answer boxes within your choice
a. -g(-θ)=□
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)
b. the function value is undefined

Explanation:

Step1: Use the property of cosine function

The cosine function is even, so \(g(-\theta)=\cos(-\theta)=\cos\theta\).

Step2: Substitute \(\theta = 45^{\circ}\)

We know that \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\). Then \(-g(-\theta)=-\cos\theta\). Substituting \(\theta = 45^{\circ}\), we get \(-\cos45^{\circ}\).

Step3: Calculate the value

\(-\cos45^{\circ}=-\frac{\sqrt{2}}{2}\)

Answer:

\(-\frac{\sqrt{2}}{2}\)