More stupid questions :)

[chickenpop]

I figured that I shouldn't be making new topics for everything I don't understand (which is a lot ), nor wanted to hijack someone else's, so I decide to make a new topic for all the stupid questions I have 

I asked this on Merspi, but no one got back to me 

Q. Find the value of tan(cos^-1 (-3/7))   

For this question, I understand that

The range for Cos-1 is [0, pi] (Q1 and Q2)
and that negative cos is (Q2 and Q3)
thus the quadrant is Q2.

However, what about questions with sin^-1 and tan^-1? What is the quadrants for them? 

[moekamo]

first let so

so if , then

so if we draw the triangle(see attached pic) then we can find the unknown side and hence find that which i hope is right :S

also the last part of your question, the range for sin-1 is [-pi/2 to pi/2]
the range for tan-1 is (-pi/2 to pi/2)

[chickenpop]

awesome, thanks moekamo. So for sin(tan^-1 (-3/7)), would the steps be

1. draw triangle
2. use pythagoras to find the missing value
3. find value through opposite/hypotenuse (sin)   
4. figure out quadrant (tan^-1 is Q1 and Q4, while -ve tan is Q2 and Q4) hence Q4
5. Q4 is -ve for sin, hence take the -ve value for step 3