Unit 2

Trigonometry

Using a Calculator to Determine Approximate Ratios

So far, only angles that are multiples of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»30«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math» and «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»45«/mn»«mo»§#176;«/mo»«/mstyle»«/math» («math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mo»§#960;«/mo»«mn»6«/mn»«/mfrac»«/mstyle»«/math» and «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac»«mo»§#960;«/mo»«mn»4«/mn»«/mfrac»«/mstyle»«/math») have been explored. The trigonometric ratios of other angles can be approximated using a calculator. The method is straightforward, but you need to ensure your calculator is in the correct mode.

Most scientific and graphing calculators have three angle modes: degrees, radians, and gradians. You may need to refer to your calculator’s instruction manual if you are not sure how to adjust the mode. On TI-83 and TI-84 calculators, this can be changed by pressing MODE and then selecting either DEGREE or RADIAN.

To approximate «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»sin«/mi»«mn»10«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math», the button sequence for most calculators is usually either


If your calculator is set to degrees, the output should be «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»0«/mn»«mi mathvariant=¨normal¨».«/mi»«mn»173«/mn»«mi»...«/mi»«/mrow»«/mstyle»«/math». So, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»sin«/mi»«mn»10«/mn»«mo»§#176;«/mo»«mo»=«/mo»«mn»0«/mn»«mi mathvariant=¨normal¨».«/mi»«mn»173«/mn»«mi»...«/mi»«/mrow»«/mstyle»«/math».

To approximate «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»tan«/mi»«mn»2«/mn»«mi mathvariant=¨normal¨».«/mi»«mn»8«/mn»«/mrow»«/mstyle»«/math», make sure your calculator is set to radians, and then use the same key sequence. If done correctly, you should find «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»tan«/mi»«mn»2«/mn»«mi mathvariant=¨normal¨».«/mi»«mn»8«/mn»«mo»=«/mo»«mo»§#8722;«/mo»«mn»0«/mn»«mi mathvariant=¨normal¨».«/mi»«mn»355«/mn»«mi»...«/mi»«/mrow»«/mstyle»«/math».

If you have difficulty determining these values with your calculator, contact your teacher.

Note: For most angles, the trigonometric ratio determined using a calculator will be approximate. You can use either an ellipsis or an approximately equal to symbol to show this. For example,