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Post a New Question | Current Questions | Chat With Live Tutors
Posted by Kate on Thursday, May 14, 2009 at 9:04pm.
Find the exact value of each expression
Cos^-1(0)
Tan^-1 sqrt(3)/3
Sin^-1(1)
Since the expressions are capitalized, I'm not sure if I have to do anything different. Any help is appreciated.
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- 12th grade- Trigonometry - Reiny, Friday, May 15, 2009 at 7:30am
I just noticed that this remained unanswered.
the caps really have no special significance.
for the first and last, look at the sine and cosine curves.
Where does the cosine curve cross the x-axis ? ---- at pi/2
so cos^-1 (0) = pi/2
similarly where is the sine curve equal to 1 ?
at pi/2
for Tan^-1 sqrt(3)/3
look at a right-angled triangle with height of √3 and base of 3
- with your calculator set to radians, divide √3 by 3 then press
2ndF TAN (or INV TAN) to get .5236 radians which is pi/6 radians or ...
repeating the sequence again in degrees
30º
After a closer look we should realize that √3/3 = 1/√3
so our triangle would have a height of 1, a base of √3, and a hypotenuse of 2
which of course are the ratios of the
30º, 60º, 90º triangle.
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