Math Problem?

Question

Could anybody explain these types of problems to me?:

"A solution set of the equation 5 sin (X) + 3 = 3 contains all multiples of:"
(1) 45 degrees
(2) 90 degrees
(3) 135 degrees
(4) 180 degrees


How would I go about completing this and other problems concerning soultion sets.
Thanks in advance.

Answer 1

The answer is (4).

For this type of problem, you have to use algebra to isolate the trig function, but you will then need to use your basic knowledge of trig to figure out appropriate values of x:

5·sin(x) + 3 = 3
==> subtract 3 from both sides
5·sin(x) = 0
==> divide by 5 on both sides
sin(x) = 0

Now, you just need to know your trig to figure out what values of x make the sine function equal zero. If you think back to the unit circle, you will remember that sine dealt with the height, and that it was defined to be zero on either end of the horizontal radii that run through the unit circle. For an illustration of this, go here:

http://www.hsu.edu/uploadedImages/Faculty/lloydm/classes/pt/UnitCircle.GIF

You should see that this is true at the listed values of 0°, 180°, and 360°, so these are all multiples of 180°. Thus, you have your answer.

Answer 2

4

Answer 3

Well, you know that the 5 sin (x) has to equal zero... so the 5 doesn't mean anything (since it's a net value of zero).

You have to make sin (x) = 0, and since sin is the ratio of the vertical side to the hypotenuse, the angle must have no vertical component. Hence only 0 degrees, 180 degrees, 360 degrees, etc. would have a sin of 0.

The answer is 4).

Answer 4

45, 90, 135, 180 | 5
9, 18, 27, 36 | 9
1, 2, 3, 4 | 2
1, 1, 3, 2

5 * 9 * 2 * 2 * 3
540

Answer: 540

Answer 5

sin(x) = (3-3)/5 or sin(x)=0.

(4) 180 degrees.

The sine wave intersects the x-axis (0) at 180 degree increments.

Answer 6

First, do a bit of algebraic simplification. This gives you sin(X) = 0, which is obviously true for X = any multiple of 180 degrees. So it is answer #4.

Answer 7

4 is the answer since 5 sin(x) + 3 = 3 means that 5 sin (X) = 0 and that means sin x = 0 and that is possible if x = 0, pi, 2 pi etc., and we know pi = 180 degrees.

Answer 8

(4) 180 degrees

5 sin (x) + 3 = 3
5 sin (x) = 0
sin (x) = 0
x = arcsin(0) = 0, 180, 360, 540....

The sin wave crosses the x-axis every 180 degrees.

Answer 9

Okay, I just did this one by trial and error and my answer was 4) 180 degrees. However I can't guarantee that the trial and error method will work for all such questions. If this was a written answer question rather than a multiple choice question, you would probably have to work it out logically rather than just trying stuff.

Answer 10

Trial and error. Try 45 degrees and see if it works. It doesn't. Try 90 degrees and see if it works. It doesn't. Repeat for the last two and you will find the answer.