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Trigonometry Examples
Step 1
Step 1.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 1.2
Split into two angles where the values of the six trigonometric functions are known.
Step 1.3
Separate negation.
Step 1.4
Apply the difference of angles identity.
Step 1.5
The exact value of is .
Step 1.6
The exact value of is .
Step 1.7
The exact value of is .
Step 1.8
The exact value of is .
Step 1.9
Simplify .
Step 1.9.1
Simplify each term.
Step 1.9.1.1
Multiply .
Step 1.9.1.1.1
Multiply by .
Step 1.9.1.1.2
Combine using the product rule for radicals.
Step 1.9.1.1.3
Multiply by .
Step 1.9.1.1.4
Multiply by .
Step 1.9.1.2
Multiply .
Step 1.9.1.2.1
Multiply by .
Step 1.9.1.2.2
Multiply by .
Step 1.9.2
Combine the numerators over the common denominator.
Step 2
Step 2.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 2.2
The exact value of is .
Step 2.3
The exact value of is .
Step 2.4
Multiply .
Step 2.4.1
Multiply by .
Step 2.4.2
Combine using the product rule for radicals.
Step 2.4.3
Multiply by .
Step 2.4.4
Multiply by .
Step 2.5
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 second quadrant.
Step 2.6
The exact value of is .
Step 2.7
The exact value of is .
Step 2.8
Multiply .
Step 2.8.1
Multiply by .
Step 2.8.2
Multiply by .
Step 3