Find the exact value of each of the following 3614 (i) sin-| | sin (i) coscos (i

Question

Find the exact value of each of the following 3614 (i) sin-| | sin (i) coscos (ii) cos (2 tan - 101 2945 1(37)) 3614 101 I) sin Sin (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) 2945 83 (ii) COS ' | COS |- (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) (ii) cos (2 tan1 A37))-O (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)

Explanation / Answer

i)

sin-1(sin (3614/101))=sin-1(sin ((3636-22)/101))

sin-1(sin (3614/101))=sin-1(sin ((36)-(22/101)))

sin-1(sin (3614/101))=sin-1(sin (-22/101))

sin-1(sin (3614/101))=-sin-1(sin(22/101))

sin-1(sin (3614/101))= -(22/101)

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ii)

cos-1(cos (2945/83))=cos-1(cos((2988-43)/83))

cos-1(cos (2945/83))=cos-1(cos(36-(43/83)))

cos-1(cos (2945/83))=cos-1(cos(-(43/83)))

cos-1(cos (2945/83))=cos-1(cos(43/83))

cos-1(cos (2945/83))=(43/83)

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iii)

cos2a =2cos2a -1

cos(2tan-1(37)) =2(cos(tan-1(37)))2 -1

cos(2tan-1(37)) =2(cos(cos-1(1/((37)2+12))))2 -1

cos(2tan-1(37)) =2(cos(cos-1(1/38)))2 -1

cos(2tan-1(37)) =2(1/38)2 -1

cos(2tan-1(37)) =2(1/38) -1

cos(2tan-1(37)) =(1/19) -1

cos(2tan-1(37)) = -(18/19)

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