Trigonometry Examples

Find the Exact Value sin(195)
Step 1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
Step 2
Split into two angles where the values of the six trigonometric functions are known.
Step 3
Separate negation.
Step 4
Apply the difference of angles identity.
Step 5
The exact value of is .
Step 6
The exact value of is .
Step 7
The exact value of is .
Step 8
The exact value of is .
Step 9
Simplify .
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Step 9.1
Simplify each term.
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Step 9.1.1
Multiply .
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Step 9.1.1.1
Multiply by .
Step 9.1.1.2
Combine using the product rule for radicals.
Step 9.1.1.3
Multiply by .
Step 9.1.1.4
Multiply by .
Step 9.1.2
Multiply .
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Step 9.1.2.1
Multiply by .
Step 9.1.2.2
Multiply by .
Step 9.2
Combine the numerators over the common denominator.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: