1. ## Trigonometric Functions

10. and are acute angles in quadrant I, with sin =7/25 and cos=5/13. Without using a calculator determine the values of sin( + ) and tan( + ).

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...

2. Originally Posted by Skoz
10. and are acute angles in quadrant I, with sin =7/25 and cos=5/13. Without using a calculator determine the values of sin( + ) and tan( + ).

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 $\displaystyle \alpha$
looks like you need to use the sum formulas

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

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

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

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

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