Find the exact solutions to the equation cos theta sin 2 th

Find the exact solutions to the equation cos theta - sin 2 theta = 0 in the interval [0, 2 pi] Given the rational function f(x) = 2x - 16/x^2 - 4x - 21 find each of the following: (a) The domain of f(x) (b) The x-intercepts (if any)

Solution

3. cos theta -sin2theta=0

cos theta -2sin theta cos theta=0

cos theta(1-2sin theta)=0

cos theta=0 , 1-2sin theta=0

theta=pi/2,3pi/2 , theta=pi/6,5pi/6

4. f(x)=(2x-16)/(x^2-4x-21) =2(x-8)/(x-7)(x+3)

domain

denominator should not be zero

(x-7)(x+3)=0

x=7,-3

domain

(-infinity,-3)U(-3,7)U(7,infinity)

x intercept

f(x)=0

2(x-8)=0

x=8

x intercept(8,0)