The Last Ratio
The Cosine Ratio is the last of our three primary trigonometric ratios. As a review go to the following google forms and test your knowledge:
Google Forms - SOH CAH TOA
The cosine ratio is the ratio of the adjacent side to the hypotenuse of a reference angle.
Google Forms - SOH CAH TOA
The cosine ratio is the ratio of the adjacent side to the hypotenuse of a reference angle.
In this lesson we applied the cosine ratio to the same style of problems that we did the other two ratios. We practices solving for unknown angles and unknown side lengths. Through these three lessons we have learnt how to use the tangent, sine and cosine ratios to solve for unknown reference angles, unknown numerators in the ratio and unknown denominator in the ratio. The math processes used for each of the ratios is the same to solve for each unknown.
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| Primary Trigonmetric Ratio Acronym. Chart Developed By Author. Click for enlarged version. |
The key difference with each ratio is the side length that corresponds to the numerator and denominator of the ratio. In the lesson we discussed the use of the acronym SOH CAH TOA to help remember the orientation of each ratio. The chart I build and we used is pictured to the left. Using SOH CAH TOA to work backwards and rebuild the ratio equations is a great way to make sure the ratios are properly orientated. I told the students that the first thing I do when I write a quiz or test using the primary trig. ratios is write the acronym at the top of my page.
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| Comparing The Sine Ratio and The Cosine Ratio Chart Developed by Author. Click for enlarged version. |
Another comparison we looked at in this lesson was the relationship between sine and cosine. As a class we built a chart that looked at how the ratio for sine and cosine was affected with increasing angle values. For sine we found that as the angle value increased the ratio increased from 0 to 1. For cosine we found that as the angle value increased the ratio decreased from 1 to 0. When comparing the two ratios we found that at each increment in the chart on the left the value of the ratio corresponded to the invert of the other's value.
Click the following link to access this lesson's video:
