### All Trigonometry Resources

## Example Questions

### Example Question #1 : Factoring Trigonometric Equations

Factor .

**Possible Answers:**

**Correct answer:**

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 #2 : Factoring Trigonometric Equations

Which of the following values of in radians satisfy the equation

**Possible Answers:**

1, 2, and 3

1 and 2

1 only

3 only

2 only

**Correct answer:**

1 only

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 #3 : Factoring Trigonometric Equations

Find the zeros of the above equation in the interval

.

**Possible Answers:**

**Correct answer:**

Therefore,

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

### Example Question #4 : Factoring Trigonometric Equations

Factor the expression

**Possible Answers:**

**Correct answer:**

We have .

Now since

This last expression can be written as :

.

This shows the required result.

### Example Question #5 : Factoring Trigonometric Equations

Factor the following expression:

**Possible Answers:**

**Correct answer:**

We know that we can write

in the following form

.

Now taking ,

we have:

.

This is the result that we need.

### Example Question #6 : Factoring Trigonometric Equations

We accept that :

What is a simple expression of

**Possible Answers:**

**Correct answer:**

First we see that :

.

Now letting

we have

We know that :

and we are given that

, this gives

### Example Question #7 : Factoring Trigonometric Equations

Factor the following expression:

**Possible Answers:**

We can't factor this expression.

**Correct answer:**

Note first that:

and :

.

Now taking . We have

.

Since and .

We therefore have :

### Example Question #21 : Understanding Trigonometric Equations

Factor the following expression

where is assumed to be a positive integer.

**Possible Answers:**

We cannot factor the above expression.

**Correct answer:**

We cannot factor the above expression.

Letting , we have the equivalent expression:

.

We cant factor since .

This shows that we cannot factor the above expression.

### Example Question #22 : Understanding Trigonometric Equations

Factor

**Possible Answers:**

**Correct answer:**

We first note that we have:

Then taking , we have the result.

### Example Question #8 : Factoring Trigonometric Equations

Find a simple expression for the following :

**Possible Answers:**

**Correct answer:**

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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