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Find the exact value of the following, without using a calculator.
sin(sin^-1 (1/2)+tan^-1 (-5))
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0. Let be = , and
let be = .
Then we have = with in QI and = -5 with in QIV, and we need to find .
Surely, we will use the formula
= , (1)
but first we shall calculate , and .
1. Since = , we have = and = . (2)
2. = = = = .
Hence, = = . (3)
We chose the sign "-" at the square root, since the angle lies in QIV (due to the sign of tan).
3. Since = , we have
= = = = = = . (4)
4. Now you have everything to use the formula (1):
= = .
Solved.
For other similar solved problems see the lesson
- Advanced problems on calculating trigonometric functions of angles
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Trigonometry: Solved problems".