Question

For question 4 and 5, what values for Ɵ (0≤Ɵ≤2π) satisfy the equation?
4. 4cosƟ+1= 2cosƟ (1 point)
a. 2π/3, 4π/3
b. π/6, 5π/6
c. 7π/6, 11π/6
d. π/3, 6π/3

5. cosƟ- tanƟ cosƟ=0 (1 point)
a. 0, π/4, π, 5π/4
b. π/4, 5π/4
c. π/2, 3π/4, 3π/2, 7π/4
d. π/2, 7π/6, 3π/2, 11π/6

Answer 1

I really need help with this, I do not understand this. If you can please show me step-by-step how you did it I would be happy. Thank you in advance.

Answer 2

Ok, for question four you have that:

4cos(theta)+1=2cos(theta)
2cos(theta)+1=0
2cos(theta)=-1
cos(theta)=-1/2

And for question five:

cos(theta)-tan(theta)cos(theta)=0
If you divide both sides for cos(theta) you will have
1-tan(theta)=0
tan(theta)=1

Do you know how to get the values of the angles now?

Answer 3

Not really.. I'm sorry, I really don't understand this stuff.

Answer 4

Did you understand the steps until now?

Answer 5

Yes

Answer 6

Do I use the unit circle?

Answer 7

Do you know what angle makes cos(theta) = 1/2?

Answer 8

No. I am really bad at math.

Answer 9

I'm sorry, but I really do need your help.

Answer 10

Ok, if I where you I will learn the values for some angles from 0 to 90º Here is a table:

http://marcsmnm.blogspot.com.es/2011/03/memorizing-common-trig-values.html

From these values you can compute the others. You know that cosine is postive in the first and the fourth quadrant of a circle, and negative in the second and the third ok?

Answer 11

Is the answer B? I was looking at the Unit Circle and I thought that might be right.

Answer 12

Now, if we know that for cos(theta)=1/2 only if theta=30º=pi/6, the values when its negative are pi/6+pi/2 and pi/6+pi so for question 4 answer is a). Is that ok? Can you do it for question 5?

Answer 13

Ummm. Okay, I'm not sure.

Answer 14

I turned it in and you where right on #4 it was a. #5 was B

Answer 15

Yes, it is. Good job!