Trigonometric Functions

Quote:

Originally Posted by Skoz

10. http://alt2.artofproblemsolving.com/...80b4948e68.gif and http://alt1.artofproblemsolving.com/...8632e2f8c4.gif are acute angles in quadrant I, with sin http://alt2.artofproblemsolving.com/...80b4948e68.gif =7/25 and coshttp://alt1.artofproblemsolving.com/...8632e2f8c4.gif=5/13. Without using a calculator determine the values of sin(http://alt2.artofproblemsolving.com/...80b4948e68.gif + http://alt1.artofproblemsolving.com/...8632e2f8c4.gif) and tan(http://alt2.artofproblemsolving.com/...80b4948e68.gif + http://alt1.artofproblemsolving.com/...8632e2f8c4.gif).

So far i did

x^2 + y^2 = r^2

x^2 + 7^2 = 25^2

x^2= 625-49
x= +- 24

im not sure if thats even right...

looks ok so far 24 is the adj side angle $\alpha$
looks like you need to use the sum formulas

$cos\alpha = \frac{24}{25}$ and $sin\beta = \frac{12}{5}$

$sin(\alpha + \beta) = sin\alpha cos\beta + cos\alpha sin\beta$

$Tan\alpha = \frac{7}{24}$

$Tan\beta = \frac{12}{5}$

$tan(\alpha + \beta) = \frac{tan\alpha + Tan\beta}{1 - tan\alpha tan\beta}$