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

B.pi/4, 5pi/4

Answer 2

are you positive? @tanya123

Answer 3

Yes.

Answer 4

could you help me with another? if you dont mind? @tanya123

Answer 5

4cos theta + 1= 2cos theta

Answer 6

Sorry I don't know this one, but I think he could help you @jim_thompson5910

Answer 7

@jim_thompson5910 can you help?

Answer 8

think of cos(theta) as 'z'

so we really have this equation

4z + 1 = 2z

solve for z to get ???

Answer 9

2?

Answer 10

no

Answer 11

4z + 1 = 2z

4*2 + 1 = 2*2

8 + 1 = 4

9 = 4 ... that equation is false, so z = 2 is not the solution

Answer 12

oh! ohkay

Answer 13

wait, so would that mean there is no answer?

Answer 14

because thats not one of my choices?

Answer 15

4z + 1 = 2z

4z = 2z - 1

4z - 2z = -1

...
...
...

z = ??

Answer 16

don't worry about the final answer

right now, we're just focusing on solving for z

Answer 17

you know what, im missing part of this problem.

what values for theta(0greater than or equal to theta greater than or equal to 2 pi) satisfy the equation

im not sure if that makes a difference

Answer 18

it does, but not for this bit when solving for z

Answer 19

2z=-1
z=-2

Answer 20

2z = -1 is right
z = -2 is NOT correct

Answer 21

hmm -1/2?

Answer 22

yes

Answer 23

we made z = cos(theta)

so what we really have is cos(theta) = -1/2

Answer 24

use a unit circle to solve for theta in cos(theta) = -1/2

Answer 25

im sorry, I don't really understand how use the unit circle

Answer 26

do you have a unit circle with you?

Answer 27

yes

Answer 28

look for points on the unit circle that have an x coordinate of -1/2

Answer 29

what's the angle that's associated with them (in radians)?

Answer 30

in quadrant III and II

Answer 31

good

Answer 32

you're in the right quadrants

Answer 33

awesome, so what next

Answer 34

locate the point in quadrant 2 has an x coordinate of -1/2

what is the angle of this point?

Answer 35

120 and 240

Answer 36

120 is in quadrant 2
240 in quadrant 3

those are the degree angles

what about the radian angles?

Answer 37

2pi/3 and 4pi/3

Answer 38

correct

Answer 39

so is that my answer?

Answer 40

yes, those are the solutions to 4cos(theta) + 1 = 2cos(theta)

Answer 41

where 0 <= theta < 2pi

Answer 42

thank you so much!

Answer 43

could you check the answer to my first question to make sure it is right?

Answer 44

can you post it again (with the answer you got)

Answer 45

yes of course