# Thread:

1. ## Radians

Hi, need help understanding 2 problems.

Give all the solutions to the following problems, answer in radians.

$\sin(3x)=\sqrt{3}/2$

and

$\cos(x-pi/4)=1/\sqrt{2}$

Thanks.

2. Originally Posted by Smifsret
Hi, need help understanding 2 problems.

Give all the solutions to the following problems, answer in radians.

$\sin(3x)=\sqrt{3}/2$

and

$\cos(x-pi/4)=1/\sqrt{2}$

Thanks.
You need to know what angle for sine gives the value $\frac{\sqrt{3}]{2}$. This happens to be $\frac{\pi}{3}$

Solve for $3x = \frac{\pi}{3}$

3. Thanks, is the second one pi / 4 then?

Does pi/4 count as an answer (if its right) or do they want me to write a number?

4. sin(3x)= pi/3

x1. sin(x) = pi/9 + 2 * pi * n?
x2. sin(x) = pi-pi/9 + 2 * pi * n?

Is that correct?

5. Ahh the question is to answer EXACTLY in radians and I was told it isn't exactly unless you write it like that.

Also the formula + n * 2 * pi I was told to add because n is the number of times it has gone around the circle.

Hope I explained that decently.

But I understand that I shouldn't have addad sin to the solution, thank you, as always I wasn't aware that it mattered.

6. For the second part

x1 = pi/2

x2 = -pi/2

Correct?

7. Originally Posted by Smifsret
Ahh the question is to answer EXACTLY in radians and I was told it isn't exactly unless you write it like that.

Also the formula + n * 2 * pi I was told to add because n is the number of times it has gone around the circle.

Hope I explained that decently.

But I understand that I shouldn't have addad sin to the solution, thank you, as always I wasn't aware that it mattered.
I'm sorry, I should have realized that your x1 and x2 were solutions to the first problem, not solutions to problems 1 and 2.

In that case, yes, those solutions are correct (with x replacing your sin(x).)

-Dan

8. You wrote that
$x - \frac{\pi}{4} = \frac{\pi}{6}$
i think that its
$1/\sqrt{2}=0.70711 = 45 degrees = \frac{\pi}{4}$

Or am I completely wrong?

9. Originally Posted by Smifsret
You wrote that
$x - \frac{\pi}{4} = \frac{\pi}{6}$
i think that its
$1/\sqrt{2}=0.70711 = 45 degrees = \frac{\pi}{4}$

Or am I completely wrong?
My apologies again. You are correct.

I'm going back to bed.

-Dan

10. Thank you very much for the help, does that mean that my previous answers were correct?
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