Question

Select the best answer.

cos(180° + θ) =
A.sinθ
B.cosθ
C.-cosθ
D.-sinθ
It is NOT cosθ.

Answer 1

The value of cos(180° + θ) is -cosθ, so the correct answer is C. This follows from the cosine sum angle identity and properties of trigonometric functions.

Step-by-step explanation:

The question is asking for the value of cos(180° + θ). This can be solved using the properties of trigonometric functions, particularly the cosine of a sum angle identity which states cos(α + β) = cos α cos β - sin α sin β. Considering α = 180° and β = θ, we can simplify:

• cos(180°) = -1 (since cosine is negative in the second quadrant),
• sin(180°) = 0 (since sine is zero at 180°).

Thus, cos(180° + θ) = cos(180°)cos(θ) - sin(180°)sin(θ) = (-1)cos(θ) - (0)sin(θ) = -cos(θ). Therefore, the correct answer is C. -cosθ.