Evaluate the following expressions. your answer must be an angle in radians and in the interval [-pi/2, pi/2]. note that pi is already provided in the answer so you just have to write the appropriate multiple. e. g. if the answer is pi/2 you should write 1/2. do not use decimal numbers. the answer should be a fraction or integer. a) sin^-1 (-square root of three/2) = ? pi b) sin^-1 (-square root of 2/2) = ? pi c) sin^-1 (-1/2) = ? pi how would i go about solving this?

A) The sine value in the parenthesis is a value for a special angle. Recall the fact that 30 or 60 degrees would have a sine or cosine value of one half or (square root of three)/2.

Since the value inside the parenthesis is negative, this means that the answer is in the fourth quadrant. The answer would just be -60 degrees or -pi/3

ANSWER: -1/3

b) The sine value inside the parenthesis for this item is also a value for a special angle. The value for a 45-degree angle or its multiples would always be (square root of 2)/2, with the sign varying depending on the quadrant.

Since we have a negative value in this item, the answer would be -45 degrees or -pi/4

ANSWER: -1/4

c) As said in the first item, one half can either be the sine or cosine value of 30 or 60 degrees. Since we are asked for the sine, we know that the angle would be 30 degrees or its multiple.

Since the sine value is negative, this would just mean that the angle is in the fourth quadrant, so the answer would be -30 degrees or -pi/6.

ANSWER: -1/6