# Thread: Trig Functions & Unit Circle

1. ## Trig Functions & Unit Circle

I have nearly no clue on how to do these kind of problems, I somewhat understand how to move the values by pi and pi/2 (kinda off sometimes) and I do know that cosine is x and sine is y

One question I want to ask first is, when adding or subtracting by pi/2, do the sine and cosine values flip and become negative or does that happen when adding pi or ?

1) Suppose cos(5) = 0.28 and sin (5) = -0.96, find an angle alpha such that cos(alpha) = 0.28 and sin(alpha) = 0.96 without using a calculator

2) If cos(t) = -3/5 and pi< t <3pi/2, find tan(t) without a calculator

3) Find a value of alpha where -3pi< alpha < -2pi

Any help is appreciated as always, I'll be sure to give you a thanks for your input

2. Originally Posted by realintegerz
One question I want to ask first is, when adding or subtracting by pi/2, do the sine and cosine values flip and become negative or does that happen when adding pi or ?
It depends on what value you are looking, but generally adding $\pi$ will result in a negative result(assuming you had a positve answer to begin with, and vice versa). so for instance if you have $\cos\left(\frac{7\pi}{4}\right) = \frac{\sqrt{2}}{2}$, now if you add $\pi$ you will basically have $\frac{11\pi}{4} =\frac{3\pi}{4}$, so taking $\cos \left( \frac{3\pi}{4} \right) = -\frac{\sqrt{2}}{2}$. now if instead of adding $\pi$ we decide to add $\frac{\pi}{2}$ we get $\frac{7\pi}{4}+\frac{\pi}{2} = \frac{9\pi}{4}=\frac{\pi}{4}$ so taking $\cos\left(\frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}=\cos\left(\frac{7\pi}{4}\right)$ you'll find more information here Unit circle - Wikipedia, the free encyclopedia

Originally Posted by realintegerz
1) Suppose cos(5) = 0.28 and sin (5) = -0.96, find an angle alpha such that cos(alpha) = 0.28 and sin(alpha) = 0.96 without using a calculator
Since we are given $\cos(5) = 0.28$ then $\cos(\alpha) = 0.28 \Rightarrow \alpha =\arccos(0.28) \Rightarrow \alpha =5$.

now for the sine function, we are give $\sin(5) = -0.96$ then $\sin(\alpha) = 0.96 \Rightarrow \alpha =\arcsin(0.96) \Rightarrow \alpha =-5$ since sine is an odd function.

Originally Posted by realintegerz
2) If cos(t) = -3/5 and pi< t <3pi/2, find tan(t) without a calculator
if we take $\tan(\arccos(x))$ we get $\frac{\sqrt{1-x^2}}{x}$ now replacing $x$ by $-\frac{3}{5}$ yields the desired result.