Trigonometry Examples

Evaluate sin(202.5)
Step 1
Rewrite as an angle where the values of the six trigonometric functions are known divided by .
Step 2
Apply the sine half-angle identity.
Step 3
Change the to because sine is negative in the third quadrant.
Step 4
Simplify .
Tap for more steps...
Step 4.1
Remove full rotations of ° until the angle is between ° and °.
Step 4.2
The exact value of is .
Step 4.3
Write as a fraction with a common denominator.
Step 4.4
Combine the numerators over the common denominator.
Step 4.5
Multiply the numerator by the reciprocal of the denominator.
Step 4.6
Multiply .
Tap for more steps...
Step 4.6.1
Multiply by .
Step 4.6.2
Multiply by .
Step 4.7
Rewrite as .
Step 4.8
Simplify the denominator.
Tap for more steps...
Step 4.8.1
Rewrite as .
Step 4.8.2
Pull terms out from under the radical, assuming positive real numbers.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: