Trigonometry Examples

Simplify sin((11pi)/4)cos((7pi)/6)+cos(11/4)sin((7pi)/6)
Step 1
Subtract full rotations of until the angle is greater than or equal to and less than .
Step 2
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 3
The exact value of is .
Step 4
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
Step 5
The exact value of is .
Step 6
Multiply .
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Step 6.1
Multiply by .
Step 6.2
Combine using the product rule for radicals.
Step 6.3
Multiply by .
Step 6.4
Multiply by .
Step 7
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 8
The exact value of is .
Step 9
Combine and .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: