Constructing Knowledge
There are three pairs of sides that can be identified from the triangle in the Getting Into It activity. They are:
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the
length opposite θ and the
length adjacent to θ
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the
length opposite θ and the
hypotenuse
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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.
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Tangent Ratio
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\(\text{tangent of angle}\,\theta=\frac{\color{blue}{\text{length opposite}\,\theta}}{\color{red}{\text{length adjacent to}\,\theta}}\)
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Sine Ratio
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\(\text{sine of angle}\,\theta=\frac{\color{blue}{\text{length opposite}\,\theta}}{\color{green}{\text{hypotenuse}}}\)
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Cosine Ratio
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\(\text{cosine of angle}\,\theta=\frac{\color{red}{\text{length adjacent to}\,\theta}}{\color{green}{\text{hypotenuse}}}\)
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Primary Trigonometric Ratios
The sine, cosine, and tangent ratios
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Sine Ratio
The ratio of the side length opposite an angle to the length of the hypotenuse in a right triangle
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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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Alberta Distance Learning Centre