# Finding exact value of trigonometric expression

• Mar 2nd 2013, 08:16 PM
vaironxxrd
Finding exact value of trigonometric expression
Hello Everyone,

I'm having a little bit of trouble with the following problem.

I need to find $\displaystyle cos(v - u)$ using $\displaystyle sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}$

I tried using those values to find the missing functions
$\displaystyle sin\ u = \frac{7}{25}, cos\ u = \frac{24}{25} \ and \ cos\ v = -\frac{3}{5}, sin\ v = \frac{4}{5}$

Then i used the following formula ...$\displaystyle cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u$ Replaced the numbers

$\displaystyle -\frac{3}{5} \cdot \frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25}$
=

$\displaystyle -\frac{44}{175}$
• Mar 2nd 2013, 09:30 PM
Prove It
Re: Finding exact value of trigonometric expression
Quote:

Originally Posted by vaironxxrd
Hello Everyone,

I'm having a little bit of trouble with the following problem.

I need to find $\displaystyle cos(v - u)$ using $\displaystyle sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}$

I tried using those values to find the missing functions
$\displaystyle sin\ u = \frac{7}{25}, cos\ u = \frac{24}{25} \ and \ cos\ v = -\frac{3}{5}, sin\ v = \frac{4}{5}$

Then i used the following formula ...$\displaystyle cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u$ Replaced the numbers

$\displaystyle -\frac{3}{5} \cdot \frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25}$
=

$\displaystyle -\frac{44}{175}$

You can't get a unique answer unless you're told something about u and v, i.e. which quadrants they lie in...
• Mar 3rd 2013, 04:39 AM
vaironxxrd
Re: Finding exact value of trigonometric expression
Quote:

Originally Posted by Prove It
You can't get a unique answer unless you're told something about u and v, i.e. which quadrants they lie in...

Both u and v lie in Quadrant 2.

In that case.

$\displaystyle sin\ u = \frac{7}{25}, \ x = -24, \ y = 7 \ r = 25$ making $\displaystyle cos\ u = -\frac{24}{25}$
$\displaystyle cos\ v = -\frac{3}{5}. \ x = - 3, \ y = 4, \ r = 5$ making $\displaystyle sin v = \frac{4}{5}$

Then $\displaystyle cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u$ Replaced the numbers

$\displaystyle -\frac{3}{5} \cdot -\frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25}$ = $\displaystyle \frac{72}{125} + \frac{28}{125}$
= $\displaystyle \frac{4}{5}$