# Thread: Trig problem solving question

1. ## Trig problem solving question

1. Given that $Sin(x) = Cos({3 \pi}{/11})$, and x lies in the second quadrant, determine the measure of x.
I would really appreciate if someone could show me how to solve this question. Thanks.

2. Originally Posted by iMan_07
I would really appreciate if someone could show me how to solve this question. Thanks.
Cosine of an angle = sine of its complement

$\cos \frac{3 \pi}{11}=\sin \left( \frac{\pi}{2}-\frac{3 \pi}{11}\right)=\sin \frac{5 \pi}{22}$

That's a Q1 angle and you want the angle in QII.

Sin is positive in Q1 and QII, so find the reference angle in QII.

$x=\pi-\frac{5 \pi}{22}=\frac{17 \pi}{22}$

3. Just one more quick question.....

been trying for a while now and still cant figure it out.

if sin(x)= 3/5

find tan(x/2)
using the ratios i found that tanx=3/4

but i dont know wht to do from there.

any help would be appreciated.

4. Originally Posted by iMan_07
Just one more quick question.....

been trying for a while now and still cant figure it out.

using the ratios i found that tanx=3/4

but i dont know wht to do from there.

any help would be appreciated.
$\tan \frac x2 = \pm \sqrt{\frac {1 - \cos x}{1 + \cos x}}$

of course, the quadrant the angle is in determines whether the answer is + or -

5. Use the identity:
$\tan{\left(\frac{x}{2}\right)} = \frac{\sin{x}}{1+\cos{x}}$

Given sine, find cosine, and use the identity to find tan(x/2).

6. Originally Posted by Chop Suey
Use the identity:
$\tan{\left(\frac{x}{2}\right)} = \frac{\sin{x}}{1+\cos{x}}$

Given sine, find cosine, and use the identity to find tan(x/2).
nice identity

7. Originally Posted by Jhevon
nice identity

You can take your identity further and multiply either the numerator or the denominator by its respective conjugate and get the identity I mentioned.

8. Originally Posted by Jhevon
$\tan \frac x2 = \pm \sqrt{\frac {1 - \cos x}{1 + \cos x}}$

of course, the quadrant the angle is in determines whether the answer is + or -

is there a way to solve using the double angle proof?

ie. tan2x?

9. Originally Posted by iMan_07
is there a way to solve using the double angle proof?

ie. tan2x?
i would not recommend it. using the half-angle formula is the simplest way i think

10. Originally Posted by Jhevon
i would not recommend it. using the half-angle formula is the simplest way i think
i understand that it is easier.....but we never covered half-angle and we're apparently not allowed to use it...double angle on the other hand, we used.....but i cant find a way to apply it to this question.

11. Originally Posted by iMan_07
i understand that it is easier.....but we never covered half-angle and we're apparently not allowed to use it...double angle on the other hand, we used.....but i cant find a way to apply it to this question.
well, if you're a glutton for punishment, you can always do

$\tan \frac x2 = \frac {\sin \frac x2}{\cos \frac x2}$

now, each of $\sin \frac x2$ and $\cos \frac x2$ can be derived using the double angle formula for $\cos 2x$

or even easier: recall that $\tan 2x = \frac {2 \tan x}{1 - \tan^2 x}$. now replace $x$ with $\frac x2$ everywhere and solve for $\tan \frac x2$

12. Originally Posted by iMan_07
i understand that it is easier.....but we never covered half-angle and we're apparently not allowed to use it...double angle on the other hand, we used.....but i cant find a way to apply it to this question.
So what if you didn't cover it? Be ahead of your class and derive the half-angle identities. And you can do it using your double angle identities. Attempt it for abit, and if you reach to it or hit a dead-end, you can go here:
http://math.ucsd.edu/~wgarner/math4c.../halfangle.htm

Using the double angle identity for tan to find tan(x/2) is just complicated and prone to error.