### All Trigonometry Resources

## Example Questions

### Example Question #247 : Trigonometry

Which is **not** a solution for for ?

**Possible Answers:**

**Correct answer:**

Using the quadratic formula gives:

or

### Example Question #248 : Trigonometry

Solve for :

**Possible Answers:**

**Correct answer:**

Solve using the quadratic formula:

### Example Question #61 : Solving Trigonometric Equations

Find the roots for

**Possible Answers:**

No solution

**Correct answer:**

No solution

To solve, use the quadratic formula:

Both and are outside of the range of the sine function, so there is no solution.

### Example Question #62 : Solving Trigonometric Equations

Solve for :

**Possible Answers:**

**Correct answer:**

Solve using the quadratic formula:

, outside the range for cosine.

according to a calculator.

The other angle with a cosine of 0.78 would be .

### Example Question #21 : Quadratic Formula With Trigonometry

Solve for :

**Possible Answers:**

**Correct answer:**

Solve using the quadratic formula:

5 is outside the range for cosine, so the only solution that works is :

according to a calculator

The other angle with a cosine of is

### Example Question #64 : Solving Trigonometric Equations

Solve for :

**Possible Answers:**

**Correct answer:**

Use the quadratic formula:

-2 is outside the range of cosine, so the answer has to come from :

according to a calculator

The other angle with a cosine of is

### Example Question #61 : Solving Trigonometric Equations

Solve the equation

for .

**Possible Answers:**

**Correct answer:**

First of all, we can use the Pythagorean identity to rewrite the given equation in terms of .

This is a quadratic equation in terms of ; hence, we can use the quadratic formula to solve this equation for .

where .

.

Now, when , and when or .

Hence, the solutions to the original equation are

### Example Question #61 : Solving Trigonometric Equations

In the interval , what values of x satisfy the following equation?

**Possible Answers:**

**Correct answer:**

We start by rewriting the term on the right hand side in terms of .

We then move everything to the left hand side of the equation and cancel.

Apply the quadratic formula:

So . Using the unit circle, the two values of that yield this are and .

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