Give the exact value of: a. cos(sin^(-1)(-.5)) b. cos^(-1)(cos 7pi /6)

Jimena Hatfield

Jimena Hatfield

Answered question

2022-09-03

Give the exact value of:
a. cos ( sin 1 ( .5 ) )
b. cos 1 ( cos 7 π / 6 )

Answer & Explanation

Kenny Kramer

Kenny Kramer

Beginner2022-09-04Added 14 answers

a) sin 1 ( 1 / 2 ) asks you to find the angle that gives you -1/2 in sin ( x ).
sine is negative in the third and fourth quadrants. The reference angle is π / 6. The answer is either 7 π / 6 or π / 6 (or 11 π / 6). Choose π / 6 to use since it is easier to work with.
cos ( π / 6 )
The reference angle is π / 6. cos ( π / 6 ) = 3 / 2; in the fourth quadrant cosine is still positive so final answer is 3 / 2 radians.
b) cos ( 7 π / 6 ) is what we found above = 3 / 2
cos 1 ( 3 / 2 ) asks at what angle is cos ( x ) = 3 / 2?
The answer is 7 π / 6.

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