Trigonometry Examples

Evaluate tan(22.5)
Step 1
Rewrite as an angle where the values of the six trigonometric functions are known divided by .
Step 2
Apply the tangent half-angle identity.
Step 3
Change the to because tangent is positive in the first quadrant.
Step 4
Simplify .
Tap for more steps...
Step 4.1
The exact value of is .
Step 4.2
Write as a fraction with a common denominator.
Step 4.3
Combine the numerators over the common denominator.
Step 4.4
The exact value of is .
Step 4.5
Write as a fraction with a common denominator.
Step 4.6
Combine the numerators over the common denominator.
Step 4.7
Multiply the numerator by the reciprocal of the denominator.
Step 4.8
Cancel the common factor of .
Tap for more steps...
Step 4.8.1
Cancel the common factor.
Step 4.8.2
Rewrite the expression.
Step 4.9
Multiply by .
Step 4.10
Multiply by .
Step 4.11
Expand the denominator using the FOIL method.
Step 4.12
Simplify.
Step 4.13
Apply the distributive property.
Step 4.14
Cancel the common factor of .
Tap for more steps...
Step 4.14.1
Cancel the common factor.
Step 4.14.2
Rewrite the expression.
Step 4.15
Combine and .
Step 4.16
Simplify each term.
Tap for more steps...
Step 4.16.1
Apply the distributive property.
Step 4.16.2
Multiply .
Tap for more steps...
Step 4.16.2.1
Raise to the power of .
Step 4.16.2.2
Raise to the power of .
Step 4.16.2.3
Use the power rule to combine exponents.
Step 4.16.2.4
Add and .
Step 4.16.3
Simplify each term.
Tap for more steps...
Step 4.16.3.1
Rewrite as .
Tap for more steps...
Step 4.16.3.1.1
Use to rewrite as .
Step 4.16.3.1.2
Apply the power rule and multiply exponents, .
Step 4.16.3.1.3
Combine and .
Step 4.16.3.1.4
Cancel the common factor of .
Tap for more steps...
Step 4.16.3.1.4.1
Cancel the common factor.
Step 4.16.3.1.4.2
Rewrite the expression.
Step 4.16.3.1.5
Evaluate the exponent.
Step 4.16.3.2
Multiply by .
Step 4.16.4
Cancel the common factor of and .
Tap for more steps...
Step 4.16.4.1
Factor out of .
Step 4.16.4.2
Factor out of .
Step 4.16.4.3
Factor out of .
Step 4.16.4.4
Cancel the common factors.
Tap for more steps...
Step 4.16.4.4.1
Factor out of .
Step 4.16.4.4.2
Cancel the common factor.
Step 4.16.4.4.3
Rewrite the expression.
Step 4.16.4.4.4
Divide by .
Step 4.16.5
Apply the distributive property.
Step 4.16.6
Multiply by .
Step 4.17
Add and .
Step 4.18
Subtract from .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: