Write each expression as a single trigonometric function 1 c

Write each expression as a single trigonometric function, 1- cos 80 1 + cos 44 b. France 1 - cos 66 V1 + cos 66 Use a half-angle identity to find exact values for sin B, cos B, and tans for the given value of = 75°. Determine the exact values for sin (9), cos (), and tan (G) when cos(0). P in Q IV. A telephone pole has two attached cables, one at a height of 42 ft and the other 10 ft. Both cables are grounded with the same stake 16 ft from the base of the le. Find cos 0. 10 ft Kjon 16 ft

Solution

a) sqrt ( 1- cos 80 / 2 )

applying half angle formula

sin ( x/2 ) = sqrt ( 1 - cos x ) / 2

so we can write

sqrt ( 1- cos 80 / 2 ) = sin ( 80/ 2)

b) sqrt ( 1 + cos 44 )/2

cos ( x/2 ) = sqrt ( 1 + cos x ) / 2

sqrt ( 1 + cos 44 )/2 = cos (44/2)

c) sqrt ( 1 - cos 66 ) / (1 + cos 66 )

= tan (66/2 )