Posted by **Claire** on Saturday, August 7, 2010 at 4:21am.

7. Evaluate sin[sin^-1(-1/2)].

a. 1/2

b. ð /6

c. -1/2

d. - ð /6

8. Evaluate cos[tan^-1(5/12)].

a. 12/13

b. 12/5

c. 5/12

d. 5/13

9. Evaluate cos[sin^-1(-3/5)].

a. -4/5

b. 5/4

c. 4/5

d. -3/4

- Inverse Functions & Trig. Equations -
**Reiny**, Saturday, August 7, 2010 at 9:01am
I don't know at what level you have studied inverse trig functions, but Sal Khan has hundreds of very simple videos on Youtube.

http://www.youtube.com/watch?v=JGU74wbZMLg

Let's look at your #9

first of all sin^-1 (-3/5) to me means ..

give me the angle Ø so that sinØ = -3/5

and since sin (of angle) = opposite/hypotenuse, I see the famous 3-4-5 triangle.

But since the sine is negative, I could sketch that triangle in quadrants III or IV,

(I will pick IV since -Ø is the smallest angle)

so now we want

cos(the angle of that triangle) = adj/hyp = 4/5

Of course you could just blindly let your calculator do the work for you ...

on mine :

2nd F

sin

(-3/5)

=

cos

=

and I got 0.8 which is 4/5

Now do #2 the same way.

BTW, wouldn't #1 be -1/2 by the

"Just look at it" Theorem ?

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