# Trigonometry : Factoring Trigonometric Equations

## Example Questions

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### Example Question #154 : Trigonometry

Factor .

Explanation:

Don't get scared off by the fact we're doing trig functions! Factor as you normally would. Because our middle term is negative (), we know that the signs inside of our parentheses will be negative.

This means that  can be factored to  or .

### Example Question #155 : Trigonometry

Which of the following values of  in radians satisfy the equation

1 and 2

3 only

1 only

1, 2, and 3

2 only

1 only

Explanation:

The fastest way to solve this equation is to simply try the three answers.  Plugging in  gives

Our first choice is valid.

Plugging in  gives

However, since  is undefined, this cannot be a valid answer.

Finally, plugging in  gives

Therefore, our third answer choice is not correct, meaning only 1 is correct.

### Example Question #156 : Trigonometry

Find the zeros of the above equation in the interval

.

Explanation:

Therefore,

and that only happens once in the given interval, at , or 45 degrees.

### Example Question #1 : Factoring Trigonometric Equations

Factor the expression

Explanation:

We have .

Now since

This last expression can be written as :

.

This shows the required result.

### Example Question #158 : Trigonometry

Factor the following expression:

Explanation:

We know that we can write

in the following form

.

Now taking ,

we have:

.

This is the result that we need.

### Example Question #2 : Factoring Trigonometric Equations

We accept that :

What is a simple expression of

Explanation:

First we see that :

.

Now letting

we have

We know that :

and we are given that

, this gives

### Example Question #2 : Factoring Trigonometric Equations

Factor the following expression:

We can't factor this expression.

Explanation:

Note first that:

and :

.

Now taking . We have

.

Since and .

We therefore have :

### Example Question #4 : Factoring Trigonometric Equations

Factor the following expression

where  is assumed to be a positive integer.

We cannot factor the above expression.

We cannot factor the above expression.

Explanation:

Letting , we have the equivalent expression:

.

We cant factor since .

This shows that we cannot factor the above expression.

### Example Question #5 : Factoring Trigonometric Equations

Factor

Explanation:

We first note that we have:

Then taking , we have the result.

### Example Question #6 : Factoring Trigonometric Equations

Find a simple expression for the following :

Explanation:

First of all we know that :

and this gives:

.

Now we need to see that:  can be written as

and since

we have then:

.

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