Trigonometry Examples

Solve for t 0.4=cos(2pit)
Step 1
Rewrite the equation as .
Step 2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 3
Simplify the right side.
Tap for more steps...
Step 3.1
Evaluate .
Step 4
Divide each term in by and simplify.
Tap for more steps...
Step 4.1
Divide each term in by .
Step 4.2
Simplify the left side.
Tap for more steps...
Step 4.2.1
Cancel the common factor of .
Tap for more steps...
Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Rewrite the expression.
Step 4.2.2
Cancel the common factor of .
Tap for more steps...
Step 4.2.2.1
Cancel the common factor.
Step 4.2.2.2
Divide by .
Step 4.3
Simplify the right side.
Tap for more steps...
Step 4.3.1
Replace with an approximation.
Step 4.3.2
Multiply by .
Step 4.3.3
Divide by .
Step 5
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 6
Solve for .
Tap for more steps...
Step 6.1
Simplify.
Tap for more steps...
Step 6.1.1
Multiply by .
Step 6.1.2
Subtract from .
Step 6.2
Divide each term in by and simplify.
Tap for more steps...
Step 6.2.1
Divide each term in by .
Step 6.2.2
Simplify the left side.
Tap for more steps...
Step 6.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 6.2.2.1.1
Cancel the common factor.
Step 6.2.2.1.2
Rewrite the expression.
Step 6.2.2.2
Cancel the common factor of .
Tap for more steps...
Step 6.2.2.2.1
Cancel the common factor.
Step 6.2.2.2.2
Divide by .
Step 6.2.3
Simplify the right side.
Tap for more steps...
Step 6.2.3.1
Replace with an approximation.
Step 6.2.3.2
Multiply by .
Step 6.2.3.3
Divide by .
Step 7
Find the period of .
Tap for more steps...
Step 7.1
The period of the function can be calculated using .
Step 7.2
Replace with in the formula for period.
Step 7.3
is approximately which is positive so remove the absolute value
Step 7.4
Cancel the common factor of .
Tap for more steps...
Step 7.4.1
Cancel the common factor.
Step 7.4.2
Rewrite the expression.
Step 7.5
Cancel the common factor of .
Tap for more steps...
Step 7.5.1
Cancel the common factor.
Step 7.5.2
Rewrite the expression.
Step 8
The period of the function is so values will repeat every radians in both directions.
, for any integer