## Trigonometric equation where you solve for theta

In the following tutorial the student will learn how to solve a trigonometric equation and solve for the possible values of * Θ* over the specified interval. The trigonometric equation is solved in the tutorial, as well as, in the attached

**document**.

(tan²Θ)(sinΘ) = 0

Notice that both tan²(Θ) and sin(Θ) are **factors** and that their **product** is 0.

This is exactly what we need to apply the **Zero Product Property**.

Ifthenxy = 0orx = 0.y = 0

In common language it means that if either x or y is 0 then the result is going to always be zero. We use this to our advantage by setting each factor equal to zero and then solving.

tan²(Θ)=0 and sin(Θ)=0

Now we fall back to what we know about the basic **trigonometric functions** and the **unit circle**.

andtan(Θ) = y/xsin(Θ) = y/r

First let’s talk about **tangent** and the ratio * y/x*. When

*is*

**Θ***radians and*

**0***radians,*

**π****is**

*y**and the ratio evaluates to*

**0***.*

**0**Now let’s talk about **sine** and the ratio * y/r*. In this case we get the same results as

**tangent**. When

*is*

**Θ***radians or*

**0***radians,*

**π***is*

**y***and the ratio again evaluates to*

**0***.*

**0**Note that this equation actually has an infinite number of solutions but is limit the interval to **[0,2π)**. The interval limits the solutions to **Θ = { 0, π }**.

You must log in to post a comment.