# Thread: Trig Identities

1. ## Trig Identities

The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
Find cosx=
cscx=

2. Originally Posted by HMV
The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
Find cosx=
cscx=
Hi HMV,

$\displaystyle \tan X=\frac{\sqrt{11}}{5}$

We know that $\displaystyle tan X = \frac{y}{x}$

That means $\displaystyle x = 5$ and $\displaystyle y = \sqrt{11}$

Now use $\displaystyle r^2=x^2 + y^2$ to solve for r.

Once you have values for x, y, and r you can substitute them into the following:

$\displaystyle \cos X = \frac{x}{r}$

$\displaystyle \csc X = \frac{r}{y}$

3. ## Trig Formulae

Hello HMV
Originally Posted by HMV
The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
Find cosx=
cscx=
$\displaystyle \tan x = \tfrac{\sqrt{11}}{5}$

Since the angle is in the first quadrant, it's an acute angle. So you can draw a right-angled triangle where the opposite side to angle $\displaystyle x$ is $\displaystyle \sqrt{11}$ and the adjacent $\displaystyle = 5$.

So the $\displaystyle \text{hypotenuse}^2 = 11 + 25 = 36$

$\displaystyle \Rightarrow \text{hypotenuse} = 6$

Can you complete it now?

Grandad