Posted by Claire on Saturday, August 7, 2010 at 4:21am.
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)].
- 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.
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 ?
Answer This Question
More Related Questions
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- Limit Calculas - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. ...
- calculus - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am ...
- Precalc/Trig - evaluate the expression assuming that cos(x)=1/7, sin(y)=1/3, sin...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- Trigonometry - Please review and tell me if i did something wrong. Find the ...
- Trig - Evaluate the following expression: sin(cos^-1(12/13)) tan(sin^-1(3/5)) I ...