Question

use the unit circle and your knowledge of special triangles to find exact values for sin 240 and cos 240. then use a calculator to check your answers. notice that calculators use parentheses around the 240 because sin and cos are functions. in text, except where the parentheses are required for clarity, they are often left out.

Answer 1

The exact values for sin 240 and cos 240 is -√3/2 and -1/2.

Visualize the angle on the unit circle:

Locate the angle 240 degrees on the unit circle. It's in the third quadrant, 60 degrees beyond the 180-degree mark.

Identify the reference angle:

The reference angle is the acute angle formed between the terminal side of 240 degrees and the x-axis. It's 60 degrees.

Relate to a special triangle:

The reference angle of 60 degrees is part of a 30-60-90 triangle, a special triangle with known side ratios: 1:√3:2.

Determine coordinates on the unit circle:

In the third quadrant, x-coordinates are negative, and y-coordinates are negative.

Using the ratios of the 30-60-90 triangle, we find the coordinates of the point on the unit circle where 240 degrees intersects:

x-coordinate (cos 240): -1/2

y-coordinate (sin 240): -√3/2

Therefore, sin 240 = -√3/2 and cos 240 = -1/2.