Trig Riddle #4: I am an angle
**
x
**
such that
. I satisfy the equation
. What angle am I?

### Guidance

Lastly, we can use the half and double angle formulas to solve trigonometric equations.

#### Example A

Solve when .

**
Solution:
**
Change
and simplify.

Set each factor equal to zero and solve.

#### Example B

Solve when .

**
Solution:
**
In this case, you do not have to use the half-angle formula. Solve for
.

Now, let’s find and then solve for by dividing by 2.

Now, the second solution is not in our range, so the only solution is .

#### Example C

Solve for .

**
Solution:
**
Pull a 2 out of the left-hand side and use the
formula.

**
Concept Problem Revisit
**

Use the double angle formula and simplify.

Under the constraint , when or when . Under this same constraint, when or when .

### Guided Practice

Solve the following equations for .

1.

2.

**
Answers
**

1.

From this we can see that there are no solutions within our interval.

2.

Set each factor equal to zero and solve.

### Practice

Solve the following equations for .