Trigonometry Examples

Solve for θ in Radians sin(theta)+cos(theta)*cot(theta)=2
Step 1
Simplify the left side.
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Step 1.1
Simplify each term.
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Step 1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.2
Multiply .
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Step 1.1.2.1
Raise to the power of .
Step 1.1.2.2
Raise to the power of .
Step 1.1.2.3
Use the power rule to combine exponents.
Step 1.1.2.4
Add and .
Step 2
Multiply both sides of the equation by .
Step 3
Apply the distributive property.
Step 4
Multiply .
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Step 4.1
Raise to the power of .
Step 4.2
Raise to the power of .
Step 4.3
Use the power rule to combine exponents.
Step 4.4
Add and .
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Apply pythagorean identity.
Step 7
Move to the left of .
Step 8
Rewrite the equation as .
Step 9
Divide each term in by and simplify.
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Step 9.1
Divide each term in by .
Step 9.2
Simplify the left side.
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Step 9.2.1
Cancel the common factor of .
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Step 9.2.1.1
Cancel the common factor.
Step 9.2.1.2
Divide by .
Step 10
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 11
Simplify the right side.
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Step 11.1
The exact value of is .
Step 12
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Step 13
Simplify .
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Step 13.1
To write as a fraction with a common denominator, multiply by .
Step 13.2
Combine fractions.
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Step 13.2.1
Combine and .
Step 13.2.2
Combine the numerators over the common denominator.
Step 13.3
Simplify the numerator.
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Step 13.3.1
Move to the left of .
Step 13.3.2
Subtract from .
Step 14
Find the period of .
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Step 14.1
The period of the function can be calculated using .
Step 14.2
Replace with in the formula for period.
Step 14.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 14.4
Divide by .
Step 15
The period of the function is so values will repeat every radians in both directions.
, for any integer