Given sin 30°use the trigonometric identities to find the exact value of each of

Question

Given sin 30°use the trigonometric identities to find the exact value of each of the following (a) cos 60 (6) cos 230 (e) cSC (d) sec 3 (a) cos 600 Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) (b) cos 230 Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) (c)CSC Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) (d) sec- Simplify your answer, including any radicals Use integers or fractions for any numbers in the expression.) 6

Explanation / Answer

sin 30 = 1/2

perpendicular = 1 , hypotenuse = 2

base = sqrt ( 4 - 1 ) = sqrt 3

a) cos 60 = sin 30

cos 60 = 1/2

b) cos^2 30 = ( sqrt 3/2 )^2

= 3/4

c) csc (pi/6) = 1 / sin pi/6

= 2

d) sec (pi/3 ) = 1 / cos pi/3

= 2

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