Trigonometry Examples

Solve for θ in Radians cos(theta)+sin(theta)*tan(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
Rearrange terms.
Step 7
Apply pythagorean identity.
Step 8
Move to the left of .
Step 9
Rewrite the equation as .
Step 10
Divide each term in by and simplify.
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Step 10.1
Divide each term in by .
Step 10.2
Simplify the left side.
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Step 10.2.1
Cancel the common factor of .
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Step 10.2.1.1
Cancel the common factor.
Step 10.2.1.2
Divide by .
Step 11
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 12
Simplify the right side.
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Step 12.1
The exact value of is .
Step 13
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Step 14
Simplify .
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Step 14.1
To write as a fraction with a common denominator, multiply by .
Step 14.2
Combine fractions.
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Step 14.2.1
Combine and .
Step 14.2.2
Combine the numerators over the common denominator.
Step 14.3
Simplify the numerator.
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Step 14.3.1
Multiply by .
Step 14.3.2
Subtract from .
Step 15
Find the period of .
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Step 15.1
The period of the function can be calculated using .
Step 15.2
Replace with in the formula for period.
Step 15.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 15.4
Divide by .
Step 16
The period of the function is so values will repeat every radians in both directions.
, for any integer