What are the values of cos(-2π/3) and sin(-2π/3) ?Show the steps.

To find the values of cos(-2π/3) and sin(-2π/3), follow these steps:

Step 1: Identify the Quadrant
The given angle is -2π/3. A negative angle means we rotate clockwise from the positive x-axis.

Convert -2π/3 into a positive reference angle:
Since π corresponds to 180°, we convert:
-2π/3 × (180°/π) = -120°

The angle -120° places us in the third quadrant, where:

cosine is negative
sine is negative
Step 2: Find the Reference Angle
The reference angle is the positive acute angle formed with the x-axis.

The reference angle for -120° is:
180° - 120° = 60° (or in radians: π - 2π/3 = π/3)
Step 3: Use Trigonometric Values
From standard trigonometric values:

cos(π/3) = 1/2
sin(π/3) = √3/2
Since -120° is in the third quadrant:

cos(-2π/3) = -cos(π/3) = -1/2
sin(-2π/3) = -sin(π/3) = -√3/2
Final Answer
cos(-2π/3) = -1/2
sin(-2π/3) = -√3/2