MHB Evaluate Trig Expressions....Part 2

[mathdad]

Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook.

1. cos 4π/3

A. We are told to graph cos 4π/3. We are in Quadrant 3.

B. Find the reference number r.

r = 3π/2 - 4π/3

r = π/6

C. Evaluate r.

cos π/6 = -sqrt{3}/2

Book's answer for r is -1/2.

2. sec 4π/3

A. We are told to graph sec 4π/3.
We are in Quadrant 3.

B. Find the reference number r.

r = 3π/2 - 4π/3

r = π/6

C. Evaluate r.

sec π/6 = -2sqrt{3}/3.

Book's answer for r is -2.

 

[skeeter]

$\dfrac{4\pi}{3}$ is in quad III $\implies$ cosine is negative

reference angle is $\dfrac{4\pi}{3} - \pi = \dfrac{\pi}{3} \implies \cos\left(\dfrac{4\pi}{3}\right) = -\cos\left(\dfrac{\pi}{3}\right) = - \dfrac{1}{2}$

 

[mathdad]

I will practice more on finding reference angles using the algebraic method you provided in Part 1, I believe. It's a very easy concept but using the graph can be a bit tricky. I prefer using algebra over graphing any time.