Find the exact value of each expression If it is defined Exp

Find the exact value of each expression, If it is defined. Express your answer in radians. (If an answer is undefined, enter UNOEHNEO.) (a) sin^-1(- squareroot2/2) (b) cos^-1(- squareroot2/2) (c) tan^-1(-1)

Solution

(a) Let sin =(-2/2) = -1/2 = sin (225⁰) or, sin (315⁰) . Then = sin^-1(-2/2) = sin^-1( -1/2)= 225⁰ or = 315⁰. ( sin is negative in the 3^rd and the 4^th quadrants; sin 45⁰ =1/2 ).

(b) Let cos =(-2/2) = -1/2 = cos (135⁰) or cos(225⁰). Then = cos^-1(-2/2)= cos^-1 (-1/2) = 135⁰ or225⁰. (cos is negative in the 2^nd and 3^rd quadrants; cos 45⁰ =1/2).

(c) Let tan = -1 = tan (135⁰) or, tan (315⁰).Then = tan^-1(-1) = 135⁰ or, 315⁰.( tan is negative in the 2nd and the 4^th quadrants; tan 45⁰ =1).