Rewrite the following as a product of trigonometric function

Rewrite the following, as a product of trigonometric functions. A) cos pi/11 - cos pi/2 A) -2 sin 13 pi/44 cos(-9 pi/44) B) -2 cos 13 pi/44 sin(-9 pi/44) C) -2 sin 13 pi/44 sin(-9 pi/44) D) -2 cos 13 pi/44 cos(-9 pi/44) Complete the sentence so the result is an identity. Let x be any real number. cos x = (cot x)() A) csc x B) tan x C) sin x D) sec x Find the missing parts of the triangle. A = 27 degree a = 35 km b = 50 km If necessary, round angles to the nearest whole number and side lengths to the nearest km. A) B_1 = 113 degree, C_1 = 40 degree, c_1 = 71 km B_2 = 13 degree, C_2 = 140 degree, c_2 = 18 km B) B = 40 degree, C = 113 degree, c = 71 km C) B_1 = 40 degree, C_1 = 113 degree, c_1 = 71 km B_2 = 140 degree, C_2 = 13 degree, c_2 = 18 km D) no such triangle Give the exact value of the expression. csc (sin^-1 18/30) A) 24/18 B) 18/24 C) 18/30 D) 30/18 Solve the equation for exact solutions over the interval [0, 2 pi]. A) {pi/2, 3 pi/2} B) {pi/4, 7 pi/4} C) {2 pi} D) {pi} Determine all solutions of the equation in radians. Find sin x/2, given that sin x = 1/4 and x terminates in 0

Solution

16) cospi/11 - cospi/2 =

Use the formula : -2sin(x+y)/2*sin(x -y)/2

cospi/11 - cospi/2 = -sin(pi/11 +pi/2)/2*sin(pi/11- pi/2)/2

= -sin(13pi/44)sin(-9pi/44)

Option c

17) cosx = cotx( )

cotx = cosx/sinx

So, to cancel out sinx in den , multiply by sinx

cosx = cotx(sinx)

Option C