Solve the given equation Enter your answers as a commasepara

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If enter NO SOLUTION.) 2 cos^2 (theta) - 5 cos (theta) + 2 = 0 theta Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If enter NO SOLUTION.) sin^2 (theta) - 6 sin (theta) - 7 = 0 theta =

Solution

1)   2 cos^2 theta - 5 cos theta + 2 =0

let cos theta = y

2 y^2 - 5y + 2 = 0

on solving we get

y = 2 , y = 1/2

cos theta = 2

theta = cos^-1 (2) ; solutions none

theta = cos^-1 (1/2); solutions - pi/3 + 2pik , 5 pi/3 + 2pi k

hence solutions are

pi/3 + 2pik , 5 pi/3 + 2pi k

2) sin^2 theta - 6 sin theta - 7 = 0

let sin theta = y

y^2 - 6y - 7 = 0

(y-7) (y+1) = 0

y = 7

y = -1

sin theta = 7

sin theta = -1

theta = sin^-1 (-1)

solutions are : 3pi/2 + 2pi k