How would you find the exact value of the six trigonometric function of 330 degrees?

Question

Samantha Abate · Accepted Answer

Use trig table of special arcs and unit circle -->
#sin 330 = sin (-30 + 360) = sin (-30) = - sin 30 = - 1/2#
#cos (330) = cos (-30 + 360) = cos (- 30) = cos 30 = sqrt3/2#
#tan 330 = sin/(cos) = (-1/2)(2/sqrt3) = - 1/sqrt3 = - sqrt3/3#
#cot 330 = 1/(tan) = -sqrt3#
#sec 330 = 1/(cos) = 2/sqrt3 = (2sqrt3)/3#
#csc 330 = 1/(sin) = - 2#

Aaliyah Abdullah · Answer

undefined To find the exact values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) of 330 degrees, you can use the unit circle.

Given that 330 degrees is in the fourth quadrant, its reference angle is 30 degrees. Using the unit circle:

- sin(330°) = -sin(30°) = -1/2
- cos(330°) = cos(30°) = √3/2
- tan(330°) = -tan(30°) = -1/√3 = -√3/3
- csc(330°) = -csc(30°) = -2
- sec(330°) = sec(30°) = 2/√3 = 2√3/3
- cot(330°) = -cot(30°) = -√3

So, the exact values of the trigonometric functions for 330 degrees are:

- sin(330°) = -1/2
- cos(330°) = √3/2
- tan(330°) = -√3/3
- csc(330°) = -2
- sec(330°) = 2√3/3
- cot(330°) = -√3