Question

Help me solve this equation between 0 and 360!

Answer 1

\[solve for 0degrees \le \theta <360 degrees\]

Answer 2

\[2\sin ^{2}3\theta=1 \]

Answer 3

If we begin with \[2\sin ^{2}3\theta=1\] and then divide both sides by 2, we get \[\sin^23 \theta=\frac{ 1 }{ 2 }\]

Taking the sqrt of both sides, \[\sin 3 \theta =\pm \frac{ 1 }{ \sqrt{2} }\]

Answer 4

Experiment. For what values of (3 theta) would the sine of (3 theta) be plus or minus 1/sqrt(2)?

Once you've answered that question, set 3 theta = to your results, and solve the following equations (there will be more than one equation) for theta. You want to find all such solutions that lie between 0 and 360 degrees.

Answer 5

so the reference angle is 45 degrees

Answer 6

so when sin is positive it is 45 and 180-45

Answer 7

then you divide by 3?

Answer 8

15 and 45 are the angles when sin is positive

Answer 9

Seems that way to me. One example would be (3 theta) = 45 degrees; you would then solve that equation for theta alone.

Answer 10

Try it. Always check your answers by substituting them back into the original equation. You are looking for values of theta between 0 and 360 degrees.

Answer 11

yup they make sense (aka I checked them)

Answer 12

Satisfied, then? How many values have you found? My educated guess is that there should be 4 solutions (values of theta).

Answer 13

so sin negative is 225/3=74 and 360-45/3=105 which is

So I have 15 45 74 105

Answer 14

but the answer is 15 45 135 165 255 and 285 degrees

Answer 15

You're going to have to figure out where those came from. Remember that the sine function is positive in the 1st and 2nd quadrants, and neg. in the 3rd and 4th.

Answer 16

yup so