How to Calculate the Cosine of a Negative Radian

There are three problems buried in taking the cosine of an angle in negative radians. The first problem is understanding the relationship between degrees and radians. The second problem is understanding negative angles. The third problem is understanding how to use your calculator or computer to find the value of the cosine. Most calculators and computer functions should have no problem with a negative number in the argument, so we'll deal with negative angles last.

Things You'll Need

• Calculator with trigonometric functions (including cosine) or
• A computer with a spreadsheet program

Instructions

Using Calculators

1. Determine if your calculator is set up to take radians or degrees as the input.

2. Take the cosine of 1. If the answer is around 0.54, the calculator is set up to assume you are entering your angle measured in radians. If the answer is around 0.999, the calculator is set up to assume your are entering your angle in degrees.

3. Take the cosine of your angle like you did for the test using 1. Only do this if the calculator is set to work with radians and your angle is in radians.

4. Multiply your angle by 0.017452 to convert degrees to radians and find the cosine if the calculator is set up to work with radians and your angle is in degrees,

5. Enter the angle and take the cosine like you did for the test using 1. Do this only if your calculator is set up to work in degrees and you have your angle in degrees.

6. Multiply the angle by 57.2958 to convert radians to degrees, then find the cosine of the angle in degrees. Do this only if your calculator is set up to work in degrees and you have an angle in radians.

Using Microsoft Excel

1. Type the following in a cell and press enter to find the cosine: @cos(-1.5). The result for this example is 0.0707. Microsoft Excel spreadsheets are set up to assume you are entering angles in radians.

2. Convert degrees to radians by using the "Radians" function. If your angle is -45 degrees, type in @radians(-45) and press "Enter." Your answer should be -0.7854.

3. Find the cosine of an angle in degrees all in one step. If your angle is -45 degrees, type in @cos(radians(-45)) and press "Enter" to get -0.7854.

4. Convert radians to degrees by using the degrees function. Suppose your angle is -1.5 radians. Type in @degrees(-1.5) and press "Enter" to get an answer of -85.9437 degrees.

Tips & Warnings

• If you draw an angle on graph paper by starting with a horizontal line, rotate counterclockwise around the left side of the line and draw another line to the left side of the line from the point where rotation is ended, you have a positive angle between the starting and ending lines. If you rotate counterclockwise, you have a negative angle. Calculators and computers can handle negative angles without problem.

References

• Math Warehouse: Converting Radians to Degrees
• Trigonometry Facts: Negative AngleUnit Circle