Question

when finding $\cos \theta = \frac{\sqrt{3}}{2}$ on a unit circle, what type of special right triangle or ray is used? (1 point) \bigcirc a vertical ray from the origin \bigcirc 45-45-90 triangle \bigcirc a horizontal ray from the origin \bigcirc 30-60-90 triangle

Explanation:

1. Recall the cosine values for special angles:

• For a 30 - 60 - 90 triangle, the cosine of 30° (or $\frac{\pi}{6}$ radians) is $\frac{\sqrt{3}}{2}$, and the cosine of 60° (or $\frac{\pi}{3}$ radians) is $\frac{1}{2}$.
• For a 45 - 45 - 90 triangle, the cosine of 45° (or $\frac{\pi}{4}$ radians) is $\frac{\sqrt{2}}{2}$.
• A vertical ray from the origin would correspond to an angle of 90° or 270°, where $\cos(90^{\circ}) = 0$ and $\cos(270^{\circ})=0$.
• A horizontal ray from the origin would correspond to an angle of 0° or 180°, where $\cos(0^{\circ}) = 1$ and $\cos(180^{\circ})=- 1$.

1. Since $\cos\theta=\frac{\sqrt{3}}{2}$, and this value is associated with the 30 - 60 - 90 triangle (because of the special angle values in this triangle), we can conclude that the 30 - 60 - 90 triangle is used.

Answer:

D. 30 - 60 - 90 triangle