# Thread: Trig with Pi?

1. ## Trig with Pi?

I have the question
a) 3sin(2pi/3) + 2tan(5pi/4)
I have to solve it without a calculator, could you explain step by step how you did it? Thanks.

2. ## Re: Trig with Pi?

You need to understand the unit circle and trig identities to solve this.

Here's a start

$\sin \frac{2\pi}{3}=\sin \frac{\pi}{3}$

and

$\tan \frac{5\pi}{4}=\tan \frac{\pi}{4}$

3. ## Re: Trig with Pi?

First of all, thank you for taking the time to help me and all, much appreciated.
To my understanding, sin (2pi/3) is pretty much a third of the unit circle located in the 2nd quadrant, then we find the RAA which makes it sin(pi/3), am I correct? Also, I have some problems visualizing the unit circle. Is there any easier way to visualize if you have a question like sin (11pi/6)?
Anyways, continuing with the question
=3sin(pi/3) + 2tan (pi/4)
=3(1/2) + 2(1)
=5/2
Is this correct?

4. ## Re: Trig with Pi?

For better visualisation, you can convert radians to degrees by the following formula:

$\theta_{R}=\frac{360^{\circ}}{2\pi}\theta_{D}$

By the way your answer is correct.

5. ## Re: Trig with Pi?

There are actually quite a few images online that can greatly assist in visualizing the unit circle.
You can see the one at Wikipedia here, but it's far from the only one available. Hope it's of use.