Find the X and Y Intercepts y=-3sin(x+pi/2)

Find the X and Y Intercepts y=-3sin(x+pi/2)
Find the x-intercepts.
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To find the x-intercept(s), substitute in for and solve for .
Solve the equation.
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Rewrite the equation as .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Subtract from both sides of the equation.
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.
Simplify the expression to find the second solution.
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Subtract from .
Move all terms not containing to the right side of the equation.
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Subtract from 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.
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Move to the left of .
Subtract from .
Find the period of .
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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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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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
Consolidate the answers.
, for any integer
, for any integer
x-intercept(s) in point form.
x-intercept(s): , for any integer
x-intercept(s): , for any integer
Find the y-intercepts.
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To find the y-intercept(s), substitute in for and solve for .
Solve the equation.
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Remove parentheses.
Simplify .
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Add and .
The exact value of is .
Multiply by .
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
List the intersections.
x-intercept(s): , for any integer
y-intercept(s):
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Name

Name one billion five hundred eighty-four million one hundred eighty-six thousand one hundred thirty-three

Interesting facts

  • 1584186133 has 4 divisors, whose sum is 1584496620
  • The reverse of 1584186133 is 3316814851
  • Previous prime number is 5189

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name two hundred eighty-eight million sixty-two thousand three hundred six

Interesting facts

  • 288062306 has 32 divisors, whose sum is 522192000
  • The reverse of 288062306 is 603260882
  • Previous prime number is 229

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

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

Interesting facts

  • 65623966 has 8 divisors, whose sum is 98528040
  • The reverse of 65623966 is 66932656
  • Previous prime number is 1109

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 43
  • Digital Root 7