# Solve for θ in Radians cos(2theta-pi/2)=-1

Solve for θ in Radians cos(2theta-pi/2)=-1
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
The exact value of is .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Solve for .
Subtract from .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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### Name

Name one billion eight hundred forty-eight million five hundred thirteen thousand two hundred forty-seven

### Interesting facts

• 1848513247 has 16 divisors, whose sum is 2150853120
• The reverse of 1848513247 is 7423158481
• Previous prime number is 1117

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name six hundred sixty-seven million three hundred thirty-two thousand two hundred eighteen

### Interesting facts

• 667332218 has 8 divisors, whose sum is 1143998112
• The reverse of 667332218 is 812233766
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name five hundred fifty-seven million nine hundred six thousand six hundred seventeen

### Interesting facts

• 557906617 has 8 divisors, whose sum is 563439240
• The reverse of 557906617 is 716609755
• Previous prime number is 181

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 46
• Digital Root 1