ASIN Function in Excel

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ASIN Function in Microsoft Excel

Part 1: Introduction

Definition: The ASIN function in Microsoft Excel returns the arcsine, or inverse sine, of a number. The arcsine is the angle whose sine is the number.

Purpose: The purpose of the ASIN function is to calculate the inverse sine of a given number. This can be useful in various mathematical and trigonometric calculations.

Syntax & Arguments:

syntax
ASIN(number)

The ASIN function syntax has the following argument:

  • Number: This is a required argument. It represents the sine of the angle you want and must be from -1 to 1.

Return value: The returned angle is given in radians from pi/2 to pi/2.

Remarks: To express the arcsine in degrees, multiply the result by 180/PI( ) or use the DEGREES function.

Part 2: Examples

Let’s look at examples of how the ASIN function can be used in business scenarios.

Example 1

Purpose of Example: To calculate the slope angle in a construction project.

Data Tables and Formulas:

ABC
1SineFormulaResult
20.5=ASIN(A2)0.523598776
30.707=ASIN(A3)0.785398163
40.866=ASIN(A4)1.047197551

Explanation: In this example, the sine values represent the slope of a construction project. The ASIN function calculates the angle of the slope in radians.

Example 2

Purpose of Example: To calculate the launch angle needed for a projectile in a game design.

Data Tables and Formulas:

ABC
1SineFormulaResult
20.342=ASIN(A2)0.352546531
30.642=ASIN(A3)0.690775527
40.984=ASIN(A4)1.396263402

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the launch angle needed for a projectile in a game design.

Example 3

Purpose of Example: To calculate the angle of incidence in a physics experiment.

Data Tables and Formulas:

ABC
1SineFormulaResult
20.125=ASIN(A2)0.125663707
30.375=ASIN(A3)0.384396104
40.625=ASIN(A4)0.690775527

Explanation: In this example, the sine values represent the height ratio to the hypotenuse in a right triangle. The ASIN function calculates the angle of incidence in a physics experiment.

Example 4

Purpose of Example: To calculate the elevation angle in a drone flight path.

Data Tables and Formulas:

ABC
1SineFormulaResult
20.258=ASIN(A2)0.265248226
30.5=ASIN(A3)0.523598776
40.866=ASIN(A4)1.047197551

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the angle of elevation in a drone flight path.

Example 5

Purpose of Example: To calculate the angle of a solar panel to maximize sunlight exposure.

Data Tables and Formulas:

ABC
1SineFormulaResult
20.342=ASIN(A2)0.352546531
30.642=ASIN(A3)0.690775527
40.984=ASIN(A4)1.396263402

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the angle of a solar panel to maximize sunlight exposure.

Example 6

Purpose of Example: To calculate the slope angle and check if it is within a safe limit for construction.

Data Tables and Formulas:

ABCD
1SineFormulaResultSafe?
20.5=ASIN(A2)0.523598776=IF(C2<0.6, “Yes”, “No”)
30.707=ASIN(A3)0.785398163=IF(C3<0.6, “Yes”, “No”)
40.866=ASIN(A4)1.047197551=IF(C4<0.6, “Yes”, “No”)

Explanation: In this example, the sine values represent the slope of a construction project. The ASIN function calculates the angle of the slope in radians. The IF function is then used to check if the calculated angle is within a safe limit for construction.

Example 7

Purpose of Example: To calculate the total angle of incidence in a physics experiment and sum them up.

Data Tables and Formulas:

ABCD
1SineFormulaResultTotal
20.125=ASIN(A2)0.125663707=SUM(C2:C4)
30.375=ASIN(A3)0.384396104
40.625=ASIN(A4)0.690775527

Explanation: In this example, the sine values represent the height ratio to the hypotenuse in a right triangle. The ASIN function calculates the angle of incidence in a physics experiment. The SUM function is then used to calculate the total angle of incidence.

Example 8

Purpose of Example: To calculate the launch angle needed for a projectile in a game design and find the maximum angle.

Data Tables and Formulas:

ABCD
1SineFormulaResultMax Angle
20.258=ASIN(A2)0.265248226=MAX(C2:C4)
30.5=ASIN(A3)0.523598776
40.866=ASIN(A4)1.047197551

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the launch angle needed for a projectile in a game design. The MAX function is then used to find the maximum launch angle.

Example 9

Purpose of Example: To calculate the angle of a solar panel to maximize sunlight exposure and find the minimum angle.

Data Tables and Formulas:

ABCD
1SineFormulaResultMin Angle
20.342=ASIN(A2)0.352546531=MIN(C2:C4)
30.642=ASIN(A3)0.690775527
40.984=ASIN(A4)1.396263402

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the angle of a solar panel to maximize sunlight exposure. The MIN function then finds the minimum angle for maximum sunlight exposure.

Example 10

Purpose of Example: To calculate the angle of a slope and round it to the nearest whole number.

Data Tables and Formulas:

ABCD
1SineFormulaResultRounded
20.5=ASIN(A2)0.523598776=ROUND(C2, 0)
30.707=ASIN(A3)0.785398163=ROUND(C3, 0)
40.866=ASIN(A4)1.047197551=ROUND(C4, 0)

Explanation: In this example, the sine values represent the slope of a construction project. The ASIN function calculates the angle of the slope in radians. The ROUND function then rounds the calculated angle to the nearest whole number.

Example 11

Purpose of Example: To calculate the angle of incidence in a physics experiment and find the average angle.

Data Tables and Formulas:

ABCD
1SineFormulaResultAverage
20.125=ASIN(A2)0.125663707=AVERAGE(C2:C4)
30.375=ASIN(A3)0.384396104
40.625=ASIN(A4)0.690775527

Explanation: In this example, the sine values represent the height ratio to the hypotenuse in a right triangle. The ASIN function calculates the angle of incidence in a physics experiment. The AVERAGE function is then used to calculate the average angle of incidence.

Example 12

Purpose of Example: To calculate the launch angle needed for a projectile in a game design and find the angle corresponding to a specific sine value using VLOOKUP.

Data Tables and Formulas:

ABCD
1SineFormulaResultLookup
20.258=ASIN(A2)0.265248226=VLOOKUP(0.5, A2:C4, 3, FALSE)
30.5=ASIN(A3)0.523598776
40.866=ASIN(A4)1.047197551

Explanation: In this example, the sine values represent the ratio of the vertical distance to the hypotenuse in a right triangle. The ASIN function calculates the launch angle needed for a projectile in a game design. The VLOOKUP function is then used to find the angle corresponding to a specific sine value.

Part 3: Tips and Tricks

  1. Remember that the ASIN function returns the result in radians. To convert it to degrees, multiply the result by 180/PI( ) or use the DEGREES function.
  2. The ASIN function will return a #NUM! Error if the number is less than -1 or greater than 1 because the sine of an angle can’t be less than -1 or greater than 1.
  3. The ASIN function is an essential tool in trigonometry. It can be used in various fields like physics, engineering, game design, etc.
  4. Always check your data to ensure it falls within the acceptable range for the ASIN function (-1 to 1).
  5. You can use the ASIN function with other Excel functions to perform more complex calculations.
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