Question

let x equals negative 16 times pi over 3 period part a: determine the reference angle of x. (4 points) part b: find the exact values of sin x, tan x, and sec x in simplest form. (6 points)

Answer 1

(a) π/3

(b) sin(x) = √3/2, tan(x) = √3, sec(x) = 2

Explanation:

You want the reference angle and some trig values for x = -16π/3.

(a) Reference angle

The reference angle the positive angle between the terminal ray and the nearest branch of the x-axis.

The angle -16π/3 represents 2 full turns of 2π and 4π/3 more in the clockwise direction from the +x axis. Its terminal ray will be clockwise from the -x axis by π/3.

The reference angle is π/3.

(b) Sin, Tan, Sec

The primary trig values for this reference angle are ...

• sin(π/3) = √3/2
• cos(π/3) = 1/2 . . . . . . sec = 1/cos
• tan(π/3) = √3

The terminal ray of x is in the 2nd quadrant, where tangent and secant are negative. The trig values of interest are ...

• sin(x) = √3/2
• tan(x) = -√3
• sec(x) = -2

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