How do I evaluate these trig ratios and expressions???

Question

1) cos^2(pi/3-cot(pi/4+sin(pi/6 answer: -1/4

2) sec(60+csc^2(pi/3

3) 3cos(17pi/6+2cos(-5pi/3 answer: -3*sqrootof3/2 +1

4) 4tan(-3pi/4+sin(-pi/4

Please explain the process and how to work the problem!!!!

Answer 1

Plug in what you know from the unit circle. Sometimes it is easier to find the standard points on the unit circle before you start.

1) cos^2(pi/3) - cot(pi/4) + sin(pi/6)

(1/2)^2 - 1 + 1/2

1/4 - 1 + 1/2

-1/4

2) sec(60) + csc^2(pi/3)

2 + (2/sqrt3)^2

2 + 4/3

6/3 + 4/3

10/3

3) 3cos(17pi/6) + 2cos(-5pi/3)

3cos(5pi/6) + 2cos(pi/3)

3(-sqrt3/2) + 2(1/2)

-3sqrt3/2 + 1

4) 4tan(-3pi/4) + sin(-pi/4)

4tan(5pi/4) + sin(7pi/4)

4(-1) + -sqrt2/2

-4 + -sqrt2/2

Hope that helps some.