Question

which of the following correctly uses the special triangles on the unit circle to determine \\( \theta \\) in degrees when \\( \cos \theta=\frac{\sqrt{2}}{2} \\)? you may assume that \\( 0^{\circ} \leq \theta \leq 180^{\circ} \\).
(1 point)
\\( 90^{circ} \\)
\\( 45^{circ} \\)
\\( 30^{circ} \\)
\\( 60^{circ} \\)

Explanation:

Step1: Recall special - angle cosine values

We know the following cosine values for special angles:

• \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\)
• \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\)
• \(\cos60^{\circ}=\frac{1}{2}\)
• \(\cos90^{\circ} = 0\)

Answer:

\(45^{\circ}\)