Answer: The reference angle of the angle 5π/3 is π/3
The angle 5π/3 is in the third quadrant.
The exact value of sin 5π/3 is -√3/2 and the exact value of cos 5π/3 is equal to -1/2.
Step-by-step explanation: To find the reference angle of an angle in standard position, we subtract the angle from the nearest multiple of π/2 that is larger than the angle. In this case, the nearest multiple of π/2 that is larger than 5π/3 is 8π/3.
8π/3 - 5π/3 = 3π/3 = π
Since π is equivalent to 180 degrees, we know that the reference angle is π - 5π/3 = π/3.
To determine which quadrant an angle is in, we look at its terminal side. In this case, the terminal side of 5π/3 lies in the third quadrant because it starts on the negative x-axis and rotates clockwise.
To find the exact values of sin 5π/3 and cos 5π/3, we use the unit circle. Starting at (1,0), we rotate clockwise by 5π/3 radians until we reach our terminal point. The x-coordinate of our terminal point is -1/2 and the y-coordinate is -√3/2. Therefore, sin 5π/3 = -√3/2 and cos 5π/3 = -1/2.
Hope this helps, and have a great day!