Question

cos theta-tan theta cos theta=0

a. 0, pi/4, pi, 5pi/4
b.pi/4, 5pi/4
c. pi/2, 3pi/4, 3pi/2, 7pi/4
d. pi/2, 7pi/6, 3pi/2, 11pi/6
I believe the answer is b but im not positive

Answer 1

@jim_thompson5910

Answer 2

its using the theta(0less than or eqal to theta less than or equal to 2 pi)

Answer 3

cos(theta) - tan(theta)*cos(theta) = 0

cos(theta) - (sin(theta)/cos(theta))*cos(theta) = 0

cos(theta) - sin(theta) = 0

cos(theta) = sin(theta)

cos^2(theta) = sin^2(theta)

cos^2(theta) = 1-cos^2(theta)

cos^2(theta)+cos^2(theta) = 1

2cos^2(theta) = 1

cos^2(theta) = 1/2

cos(theta) = sqrt(1/2) or cos(theta) = -sqrt(1/2)

cos(theta) = sqrt(2)/2 or cos(theta) = -sqrt(2)/2

theta = arccos(sqrt(2)/2) or theta = arccos(-sqrt(2)/2)

theta = pi/4 or theta = 5pi/4 ... use a unit circle here




So you are correct.

Answer 4

awesome thank you so much

Answer 5

np