# Sum and difference identitiees?

• Feb 7th 2011, 07:16 PM
homeylova223
Sum and difference identitiees?
Hello! I have two problems I need help on.
use sum or difference to find the exact value of each trigonometric function.

cot 113pi/12
I know this equals= 4(360)+255
and 255 is 210+45

So I did
cot(210)+cot(45)/(1-cot(210)(cot45)
Which gives me -3.739 But I am quite sure this is wrong.(Giggle)

my second problem is
cos(x+y)= tanx(5/3) and sin y=1/3
I am quite confused on this one

Can anyone help me with these problems?
• Feb 7th 2011, 07:18 PM
homeylova223
Also for my second problem it has to be between 0<x<pi/2 0<y<pi/2
• Feb 7th 2011, 08:08 PM
pickslides
Quote:

Originally Posted by homeylova223
cot 113pi/12
I know this equals= 4(360)+255
and 255 is 210+45

The period for $\displaystyle \tan\theta$ is $\displaystyle \pi$ not $\displaystyle 2\pi$

$\displaystyle \cot \left(\frac{113\pi}{12}\right) = \frac{1}{\tan \left(\frac{113\pi}{12}\right)} = \frac{1}{\tan \left(\frac{(108+5)\pi}{12}\right)}= \frac{1}{\tan \left(\frac{5\pi}{12}\right)}$

Then use the difference formula on the following.

$\displaystyle \tan \left(\frac{5\pi}{12} \right)=\tan \left(\frac{8\pi-3\pi}{12} \right)=\tan \left(\frac{8\pi}{12}-\frac{3\pi}{12} \right)=\tan \left(\frac{2\pi}{3}-\frac{\pi}{4} \right)=\dots$
• Feb 8th 2011, 07:10 PM
homeylova223
I have another quick question well actually 2
My first one is to find the sec(1275 degrees)
I have sec(1275)= 3(360)+195
sec(135)sec(60)+csc(135)csc(60)
I got -1.193 Did I do this one right?

On my second problem
cos(x+y)= tanx(5/3) and sin y=1/3
I did square root 1-(1/3)^2 and I got cosy= .942

Then I solved the triangle using tanx(5/3) and I got cosx=.514

I know siny= 1/3

So I did square root 1-.514^2 and got sinx= .8577

So I guess to find answer I must do cos(.514)cos(.942)+sin(.8577)sin(1/3)?