Trigonometry Examples

Evaluate sec((19pi)/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. Make the expression negative because secant is negative in the third quadrant.
Step 3
The exact value of is .
Step 4
Multiply by .
Step 5
Combine and simplify the denominator.
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Step 5.1
Multiply by .
Step 5.2
Raise to the power of .
Step 5.3
Raise to the power of .
Step 5.4
Use the power rule to combine exponents.
Step 5.5
Add and .
Step 5.6
Rewrite as .
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Step 5.6.1
Use to rewrite as .
Step 5.6.2
Apply the power rule and multiply exponents, .
Step 5.6.3
Combine and .
Step 5.6.4
Cancel the common factor of .
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Step 5.6.4.1
Cancel the common factor.
Step 5.6.4.2
Rewrite the expression.
Step 5.6.5
Evaluate the exponent.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: