Question

Find the exact trigonometric ratios for the angle x whose radian measure is given by 4π/3.

Answer 1

The trigonometric ratios for the angle 4π/3 are sine = -√3/2, cosine = -1/2, and tangent = -√3.

To find the trigonometric ratios for an angle with radian measure of 4π/3, we can use the unit circle.

• The sine ratio is equal to the y-coordinate of the point on the unit circle corresponding to the angle, so sine of 4π/3 is -√3/2.
• The cosine ratio is equal to the x-coordinate of the point on the unit circle corresponding to the angle, so cosine of 4π/3 is -1/2.
• The tangent ratio is equal to the sine divided by the cosine, so tangent of 4π/3 is (√3/2) / (-1/2) = -√3.