Trigonometry Examples

Find the Exact Value sin(105)
Step 1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 2
Split into two angles where the values of the six trigonometric functions are known.
Step 3
Apply the sum of angles identity.
Step 4
The exact value of is .
Step 5
The exact value of is .
Step 6
The exact value of is .
Step 7
The exact value of is .
Step 8
Simplify .
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Step 8.1
Simplify each term.
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Step 8.1.1
Multiply .
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Step 8.1.1.1
Multiply by .
Step 8.1.1.2
Multiply by .
Step 8.1.2
Multiply .
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Step 8.1.2.1
Multiply by .
Step 8.1.2.2
Combine using the product rule for radicals.
Step 8.1.2.3
Multiply by .
Step 8.1.2.4
Multiply by .
Step 8.2
Combine the numerators over the common denominator.
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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