Inverse Functions & Trig. Equations
posted by Claire .
7. Evaluate sin[sin^-1(-1/2)].
b. ð /6
d. - ð /6
8. Evaluate cos[tan^-1(5/12)].
9. Evaluate cos[sin^-1(-3/5)].
I don't know at what level you have studied inverse trig functions, but Sal Khan has hundreds of very simple videos on Youtube.
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 :
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 ?