A Few Trig Questions

[caharris]

1) Find each exact value of sin(x+y) if sin x=[math] \frac{3}{5}[/math] and sin y= [math] \frac{12}{37}[/math]

 

I used the sin(x+y)=(sin x)(cos y)+(cos x)(sin y) formula, [math] \frac{3}{5} * \frac{35}{37} + \frac{4}{5}*\frac{12}{37}[/math] and got [math] \frac{153}{185}[/math] as a final answer. I'm second guessing my work because the answer doesn't seem like something my teacher would give.

 

2) How would I go about finding the ArcTan of 3? I know it's 71deg-ish, but I don't know how they got that...

 

(Sorry about all the edits for this part of the post.)

 

There might be more, I'm done with fifteen out of twenty problems.

 

Thank you all for your help!

Edited November 6, 2010 by caharris

[D H]

Emphasis mine:

1) Find each exact value of sin(x+y) if sin x=[math] \frac{3}{5}[/math] and sin y= [math] \frac{12}{37}[/math]

You've found one. There are more solutions. Your teacher apparently is not as easy as you thought.

Edited November 6, 2010 by D H

[caharris]

Oh, I thought that the "each" was just there to throw me off...

[alpha2cen]

1)First, draw rectangular triangle.

sin x =3/5 ---> vertical line is 3 and leg line is 5.

Find the base line length using Teorema de Pitagoras.

5^2 = 3^2 + X^2

cos x = ?

sin y = 12/37

same method above.

cos y = ?

sin(x+y)=?

 

2)Arc tan X =3

First, draw rectangular triangle.

base line =1, vertical line =3

Using protractor.

angle=?