Question

What are all the approximate solutions for the following equation for values of t on the interval [0,2*Pi)?

7*cos(2t)+3=0

Use algebra, reference angles and inverse trig functions, accurate to 4 decimal places.

How many solutions should I get?

Answer 1

I graphed this and can see that the midline is y = 3.
Pi/2 = -4, Pi/4 = 3, Pi/3 = -1/2, Pi/6 = 13/2

Answer 2

Or should I be doing like solve for t?

Answer 3

cos2t=-3/7
2t=2.0137
t=1.007

Answer 4

You should get 4 solutions.

Answer 5

4 of them?

Answer 6

I just did the algebra and looked up and saw your solution too. It is same as what I got.

Answer 7

Well, I would think you would solve for t since the problem says: "What are all the approximate solutions for the following equation for values of t on the interval [0,2*Pi)?"

Answer 8

0, Pi/2, Pi/ 3*Pi/2???

Answer 9

Yes. 4 solutions. For cos2t=-3/7, there should be a value in quadrant 2 and another one in quadrant 4. But since it is 2t, you want to add 2pi to each of those solutions because when you divide by two to find t, the answers will be between 0 and 2pi

Answer 10

Okay, Q2 and Q4 make sense.

Answer 11

4.1484?

Answer 12

so if cos2t = -3/7, then 2t = 2.0137, 4.2695, 8.2969,10.5527
So t = 1.007, 2.1348,4.1484,5.2764

Answer 13

How did you get the 2.1348 and the 5.2764? I am totally confused...

Answer 14

I am trying a few things and do not get how the other two answers work. :(

Answer 15

If the angle in the second quadrant is (for 2t) is 2.0137 then the reference angle is pi -2.0137 or 1.1279. So there is another angle in the third quadrant with the same reference angle and it is pi +1.1279 or 4.2695.

Answer 16

Are you with me so far?