# Trig Identity math question.

#### HBK

In TrianglePQR:

3sinP + 4 CosQ= 6
and
SinQ +3 CosP= 1

a)find Sin(P+Q)
b)Determine the measure of angle R in radians.

If any one can help me solve this, I would really appreaciate it!

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#### pickslides

MHF Helper
Have you seen this?

$$\displaystyle a \sin x + b \cos x= \sqrt{a^2+b^2}\sin(x+\psi) , \psi = \arctan\left(\frac{a}{b}\right)$$

HBK

No I haven't.

#### pickslides

MHF Helper
Now you have, try to apply it to your problem.

#### HBK

Ok, I will give it a shot.

#### HBK

Sorry for the double post, what would I use for Y.

#### pickslides

MHF Helper
Using a and b

Have you seen this?

$$\displaystyle \psi = \arctan\left(\frac{a}{b}\right)$$

#### HBK

Ok thanks! I really need this problem solved. Hopefully this works out!

#### HBK

I still cant work it out!