ITF - Solving Equations Lesson

Solving Equations

Now, we will use what we know about inverse trig to solve equations. When solving trigonometric equations, it is very important to read the instructions fully so that you know the specific restrictions on the domain that apply for your problem.

Example

Find all angles that satisfy the equation $\sin\theta=\frac{\sqrt[]{2}}{2}$.

1. Using our unit circle, we know that $\theta=\frac{\pi}{4}$ and $\theta=\frac{3\pi}{4}$ are possible answers.

2. However, we know that all co-terminal angles of  and  will be answers as well, so we must write a statement that includes those.

3. Those statements look like this: $\theta=\frac{\pi}{4}+2\pi n$ and $\theta=\frac{3\pi}{4}+2\pi n$, where n is an integer.

 

Watch this video to try another problem:

Try these problems to see if you've got it.

 

Find all angles that satisfy the equations below:

 

But, sometimes you'll be given a restricted domain. Like this problem:

Find all angles, $0\le\theta\le2\pi$, that satisfy the equation $\cos\theta=-\frac{\sqrt[]{2}}{2}$.

• Solution:  $\theta=\frac{3\pi}{4}\:and\:\theta=\frac{5\pi}{4}$

 

Watch this video to try another problem.

Try these problems to see if you've got it.

 

Find all angles in the interval $0\le\theta\le4\pi$ that satisfy the equations below:

 IMAGES CREATED BY GAVS