Given the angle measure A, B, C, D,
cos
⁡
(
𝜃
)
appears equal to the cosine of which angle measure?

Question

Given the angle measure A, B, C, D, 
cos
⁡
(
𝜃
)
 appears equal to the cosine of which angle measure?

BlackTom AI · Accepted Answer

To compare cos(θ) with the cosines of the given angles, recall that on the unit circle, cosine corresponds to the x-coordinate of the point at that angle. Therefore, angles whose terminal radii have the same x-coordinate projection will have the same cosine value.

Option A: If A were the matching angle, we would expect the terminal radius for A to lie at the same vertical line (same x-coordinate) as θ. However, in the diagram A lies on a different ray than θ, so its x-coordinate projection differs, making cos(A) generally not equal to cos(θ).

Option B: The angle labeled B is located on the opposite side of the circle relative to θ, implying its terminal point has a different x-coordinate sign or magnitude. Unless B lies on the same vertical line as θ (which the diagram does not indicate), cos(B) would differ from cos(θ).

Option C: The angle labeled C appears symmetrically positioned across the horizontal diameter relative to θ. In a circle, angles that are mirror images across the x-axis share the same x-coordinate of their terminal points, hence the same cosine value. This symmetry preserves the cosine even as the angle moves to the opposite side.

Option D: The angle labeled D is located on a different ray, likely producing a different x-coordinate projection from θ. Thus cos(D) would generally not equal cos(θ).

In summary, because cosine is the x-coordinate and is preserved under reflection across the horizontal axis, the angle whose terminal point has the same x-coordinate as θ is the one mirrored across the horizontal diameter, which corresponds to option C.

MATH 1151 AU2025 (18443) Calculus Concept Readiness Assessment (CCR)

Given the angle measure A, B, C, D, cos ⁡ ( 𝜃 ) appears equal to the cosine of which angle measure?

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