# Find all solutions

• Mar 9th 2010, 05:28 PM
purplec16
Find all solutions
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$\displaystyle cos\theta=\frac{1}{sec\theta}$

$\displaystyle cos\theta sec\theta=1$

Is this right so far?, what is my next step
• Mar 9th 2010, 05:54 PM
Prove It
Quote:

Originally Posted by purplec16
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$\displaystyle cos\theta=\frac{1}{sec\theta}$

$\displaystyle cos\theta sec\theta=1$

Is this right so far?, what is my next step

This is not an equality that you can solve for $\displaystyle \theta$ with. It's an identity.

In other words

$\displaystyle \cos{\theta} = \frac{1}{\sec{\theta}}$ for ALL $\displaystyle \theta$, provided that the denominator does not equal $\displaystyle 0$.
• Mar 9th 2010, 06:15 PM
purplec16
I still dont get it so I have to solve it first then find the solutions?
• Mar 9th 2010, 06:32 PM
Prove It

ANY number $\displaystyle \theta$ will satisfy this equation because IT IS AN IDENTITY. (as long as the number $\displaystyle \theta$ doesn't make the denominator $\displaystyle = 0$.)
• Mar 10th 2010, 12:37 AM
Quote:

Originally Posted by purplec16
How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
$\displaystyle cos\theta=\frac{1}{sec\theta}$

$\displaystyle cos\theta sec\theta=1$

Is this right so far?, what is my next step

Hi purplec16,

$\displaystyle \frac{1}{cos\theta}$ is $\displaystyle sec\theta$

"They" are equal for all $\displaystyle \theta$
as they are one and the same.

As $\displaystyle cos\theta$ ranges from -1 to 1 $\displaystyle sec\theta$ is never zero.
• Mar 10th 2010, 06:15 AM
purplec16
I thought the range of cos is 0 to 2pi?
• Mar 10th 2010, 08:34 AM
the angle $\displaystyle \theta$ ranges from 0 to $\displaystyle 2{\pi}$ over one period
and $\displaystyle Cos\theta$ ranges from -1 to 1