# Solve for ? 5sin(x)+1=3sin(x)

Solve for ? 5sin(x)+1=3sin(x)
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
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### Name

Name eight hundred fourteen million nine hundred seventy-seven thousand thirty-four

### Interesting facts

• 814977034 has 16 divisors, whose sum is 1239533568
• The reverse of 814977034 is 430779418
• Previous prime number is 167

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 43
• Digital Root 7

### Name

Name one billion eighty-one million three hundred sixty-five thousand six hundred sixty-nine

### Interesting facts

• 1081365669 has 8 divisors, whose sum is 1204117120
• The reverse of 1081365669 is 9665631801
• Previous prime number is 463

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 45
• Digital Root 9

### Name

Name one billion three hundred nineteen million eight hundred twenty-six thousand eight hundred twenty-nine

### Interesting facts

• 1319826829 has 8 divisors, whose sum is 1346180472
• The reverse of 1319826829 is 9286289131
• Previous prime number is 961

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 49
• Digital Root 4