Right triangles: Given that ??? = sin?1 ( ), evaluate cos ???, tan???, cot ???, sec???, and csc???. Right-triangle relationships: ?Draw a right triangle to simplify the given expression Assume x?> 0 ?and 0 ????/?2.

Step-by-step solution 37RE Step 1 Given that = sin ( ) , we need to find cos , tan ,cot , sec and 13 csc assuming x > 0 and 0 . 2 Step 2 Let us assume that lies in the first quadrant, where all trigonometric functions are positive. Given: 1 12 = sin ( )13 sin = 12 [1] 13 Next, we solve for cos by using the following identity: cos = 1sin 2 [2] Substituting [1] into [2], we have, 2 12 2 cos = 1( ) 13 cos = 1 144 169 2 25 cos = 169 25 cos = 169 5 cos = 13 [3] Step 3 Next, we solve for tan by using the following property: tan = cos [4] Substituting [1] and [3] into [4], we have, 12 tan = 53 13 tan = 12 [5] 5 Step 4 Next, we solve for cot by using the following property: cot = 1 [6] tan Substituting [5] into [6], we have, cot = 12 5 cot = 12 [7]