A: The Sine and Cosine Ratios
There are three pairs of sides that can be identified from the triangle in the Warm Up. These are
-
the
length opposite θ and the
length adjacent to θ
-
the length opposite θ and the
hypotenuse
-
the
length adjacent to θ and the
hypotenuse
These side pairings are used in the three
primary trigonometric ratios, which include the tangent ratio, the
sine ratio, and the
cosine ratio.
Key Lesson Marker
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Tangent Ratio
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mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathcolor=¨#DC2515¨»adjacent«/mi»«mo mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#DC2515¨»§#952;«/mi»«/mrow»«/mfrac»«/math»
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Sine Ratio
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mathcolor=¨#00A2E8¨»opposite«/mi»«mo mathcolor=¨#00A2E8¨»§#160;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#00A2E8¨»§#952;«/mi»«/mrow»«mi mathcolor=¨#009D56¨»hypotenuse«/mi»«/mfrac»«/math»
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Cosine Ratio
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mathcolor=¨#DC2515¨»adjacent«/mi»«mo mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#DC2515¨»§#952;«/mi»«/mrow»«mi mathcolor=¨#009D56¨»hypotenuse«/mi»«/mfrac»«/math»
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Primary Trigonometric Ratios
The sine, cosine, and tangent ratios
Sine Ratio
The ratio of the side length opposite an angle to the length of the hypotenuse in a right triangle
Cosine Ratio
The ratio of the side length adjacent to an angle to the length of the hypotenuse in a right triangle
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You may have noticed that six ratios are possible for any angle in a triangle. These are:
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mathvariant=¨normal¨ mathcolor=¨#00A2E8¨»§#952;«/mi»«/mrow»«mrow»«mi mathcolor=¨#DC2515¨»length«/mi»«mo mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathcolor=¨#DC2515¨»adjacent«/mi»«mo mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathvariant=¨normal¨
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mathvariant=¨normal¨ mathcolor=¨#00A2E8¨»§#952;«/mi»«/mrow»«mi mathcolor=¨#009D56¨»hypotenuse«/mi»«/mfrac»«/math» |
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mathcolor=¨#DC2515¨»§#160;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#DC2515¨»§#952;«/mi»«/mrow»«/mfrac»«/math» |
Why do you think this course uses only three of these ratios? You will need to explain this in the Practice for this lesson.
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Before continuing with the lesson, try to determine the value of x and y using the sine and cosine ratios.
