The document discusses trigonometric ratios and their properties. It defines the three basic trigonometric ratios - sine, cosine, and tangent - for any angle. It also discusses reciprocal ratios like cosecant, secant, and cotangent, which are the reciprocals of the basic ratios. The document provides examples of calculating trigonometric ratios for various angles and triangles. It also examines ratios of complementary and special angles like 0, 30, 45, 60, 90 degrees.

1. Ihr Logo
Trigonometric
Ratios

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Outline:
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The Three Trigonometric Ratios

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Example 4.1:

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Example 4.2:
Determine the three basic trigonometric ratios
for the two angles M and N.

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Reciprocal and Complementary Angles

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Example 4.3:

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Example 4.4:
Determine the three reciprocal ratios for the
two angles M and N.

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Do you notice anything with
the definitions of secant,
cosecant, and cotangent? How
are they related to the three basic
trigonometric ratios?

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Thus, cosecant is the reciprocal
ratio of sine; secant is the reciprocal
ratio of cosine; and cotangent is the
reciprocal ratio of tangent.
Then, cosecant, secant, and
cotangent are called reciprocal
ratios.

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Ratios of Complementary Angles

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Example 4.5:

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Trigonometric Ratios of the Special Angles

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Applying the Pythagorean theorem,

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The reciprocal ratios are

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The reciprocal ratios are

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Applying the Pythagorean theorem,

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The reciprocal ratios are

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Trigonometric Ratios of Special Angles

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Example 4.6:

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Example 4.7:
Solve for x and y in the given
triangle. Determine the six trigonometric
ratios.

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