Trigonometry Examples

Find Trig Functions Using Identities sin(theta)=5/6 , cos(theta)=( square root of 11)/6
,
Step 1
To find the value of , use the fact that then substitute in the known values.
Step 2
Simplify the result.
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Step 2.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.2
Cancel the common factor of .
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Step 2.2.1
Cancel the common factor.
Step 2.2.2
Rewrite the expression.
Step 2.3
Combine and .
Step 2.4
Multiply by .
Step 2.5
Combine and simplify the denominator.
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Step 2.5.1
Multiply by .
Step 2.5.2
Raise to the power of .
Step 2.5.3
Raise to the power of .
Step 2.5.4
Use the power rule to combine exponents.
Step 2.5.5
Add and .
Step 2.5.6
Rewrite as .
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Step 2.5.6.1
Use to rewrite as .
Step 2.5.6.2
Apply the power rule and multiply exponents, .
Step 2.5.6.3
Combine and .
Step 2.5.6.4
Cancel the common factor of .
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Step 2.5.6.4.1
Cancel the common factor.
Step 2.5.6.4.2
Rewrite the expression.
Step 2.5.6.5
Evaluate the exponent.
Step 3
To find the value of , use the fact that then substitute in the known values.
Step 4
Simplify the result.
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Step 4.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.2
Multiply by .
Step 4.3
Multiply by .
Step 4.4
Combine and simplify the denominator.
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Step 4.4.1
Multiply by .
Step 4.4.2
Move .
Step 4.4.3
Raise to the power of .
Step 4.4.4
Raise to the power of .
Step 4.4.5
Use the power rule to combine exponents.
Step 4.4.6
Add and .
Step 4.4.7
Rewrite as .
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Step 4.4.7.1
Use to rewrite as .
Step 4.4.7.2
Apply the power rule and multiply exponents, .
Step 4.4.7.3
Combine and .
Step 4.4.7.4
Cancel the common factor of .
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Step 4.4.7.4.1
Cancel the common factor.
Step 4.4.7.4.2
Rewrite the expression.
Step 4.4.7.5
Evaluate the exponent.
Step 4.5
Cancel the common factor of .
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Step 4.5.1
Cancel the common factor.
Step 4.5.2
Rewrite the expression.
Step 5
To find the value of , use the fact that then substitute in the known values.
Step 6
Simplify the result.
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Step 6.1
Multiply the numerator by the reciprocal of the denominator.
Step 6.2
Multiply by .
Step 6.3
Multiply by .
Step 6.4
Combine and simplify the denominator.
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Step 6.4.1
Multiply by .
Step 6.4.2
Raise to the power of .
Step 6.4.3
Raise to the power of .
Step 6.4.4
Use the power rule to combine exponents.
Step 6.4.5
Add and .
Step 6.4.6
Rewrite as .
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Step 6.4.6.1
Use to rewrite as .
Step 6.4.6.2
Apply the power rule and multiply exponents, .
Step 6.4.6.3
Combine and .
Step 6.4.6.4
Cancel the common factor of .
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Step 6.4.6.4.1
Cancel the common factor.
Step 6.4.6.4.2
Rewrite the expression.
Step 6.4.6.5
Evaluate the exponent.
Step 7
To find the value of , use the fact that then substitute in the known values.
Step 8
Simplify the result.
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Step 8.1
Multiply the numerator by the reciprocal of the denominator.
Step 8.2
Multiply by .
Step 9
The trig functions found are as follows: