What are the key concepts for solving trigonometric functions?

[sweetcomedygirl]

Let f be the function defined by f(x) = sin(x)^2 - sin(x) for
0 < x < 3π/2
a. Find the x-intercepts of the graph of f.
b. Find the intervals on which f is increasing.
c. Find the absolute maximum value and the absolute minimum value of f.

______________

I found the x-intercepts to be x=0, π/2, and π, but for part b I know I need to take the derivative of f(x), but I don't know how, and when I tried to do so on my calculator I couldn't decipher the graph that it was showing me.

 

[colby2152]

f(x) = sin^2(x) - sin(x)
f&#039;(x) = 2sin(x)cos(x) - cos(x)
2sin(x)cos(x) - cos(x) = 0
cos(x)(2sin(x) - 1) = 0
Solve for cos(x) = 0 & sin(x) = 0.5

Then you need to test values for all x values that satisfy those equations within the boundary 0 &lt; x &lt; \frac{3\pi}{2}

 

[rebecca]

trig question

I was trying to prove the identity of cos(A+B)= Cos A Cos B - Sin A Sin B, i couldn't do it. Would u be able to direct me step by step to prove that .

 

[EnumaElish]

sweetcomedygirl: in (c), how are abs. min. and abs. max. defined?

rebecca: You can start with the attached figure. Then, you can write sin α/cos α in terms of cos β, sin β, and cos(α+β)/sin α.