# Solve for θ in Degrees sin(theta)-sin(2theta)=0

Solve for θ in Degrees sin(theta)-sin(2theta)=0
Simplify each term.
Apply the sine double-angle identity.
Multiply by .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
The exact value of is .
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.
Subtract from .
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 .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
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.
Dividing two negative values results in a positive value.
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 .
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.
Subtract from .
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 .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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### Name

Name nine hundred sixty-three million five hundred twenty-two thousand six hundred forty-five

### Interesting facts

• 963522645 has 8 divisors, whose sum is 1043098240
• The reverse of 963522645 is 546225369
• Previous prime number is 67

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name one billion eight hundred eighty-five million eight hundred eighty-eight thousand two hundred sixty-two

### Interesting facts

• 1885888262 has 8 divisors, whose sum is 2871053976
• The reverse of 1885888262 is 2628885881
• Previous prime number is 67

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 56
• Digital Root 2

### Name

Name one hundred seventy-five million three hundred seventy-four thousand nine hundred fifty-four

### Interesting facts

• 175374954 has 32 divisors, whose sum is 363444480
• The reverse of 175374954 is 459473571
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9