Expert: Sherry Wallin - 11/7/2009

Question
I need help with this problem, please!

Find the exact value of tan(sin^-1(-square root of 3 divided by 2))).

Thank you!

Answer
First things first. The sine of angle is a number but the inverse sine of a number is an angle. So you are hunting for the tangent of an angle. The first thing you need to do is decide what angle in between 0 and 90 gives the sine of the angle to be sqrt3/2. And that angle is 60 degrees. But you have -sqrt3/2 so where will y be negative? (I say this because you can think of the sine of angle being your y coordinate and the cosine of an angle being your x coordinate.) Y is negative in the 3rd and 4th quadrant. So you want the tan 240 degrees = tan 4pi/3 or the tan of 300 degrees = tan 5pi/3. You must have been given more information about where the angle is because the tangent of 240 is a positive number and the tangent of 300 degrees is a negative number. Usually problems state that the angle for tangent is between pi/2 and -pi/2. If that be this case then we would want the tan 240 deg = tan 4pi/3. Either way the |tan 4pi/3| = |tan 5pi/3| = sqrt 3

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