7.2 Right Triangle Trigonometry

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7.2 Right Triangle Trigonometry

• In this section, we will study the following
  topics
• Evaluating trig functions of acute angles using
  right triangles
• Use Fundamental Identities
• Use the Complimentary Angle Theorem

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The sides of a right triangle
Take a look at the right triangle, with an acute
angle, ?, in the figure below. Notice how the
three sides are labeled in reference to ?.

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Trigonometric Functions

• We will be reviewing special ratios of these
  sides of the right triangle, with respect to
  angle, ?.
• These ratios are better known as our six basic
  trig functions
• Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent

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Six Trigonometric Functions
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Definitions of the Six Trigonometric Functions
To remember the definitions of Sine, Cosine and
Tangent, we use the acronym SOH CAH
TOA
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Find the value of each of the six trigonometric
functions of the angle ?.
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Example
Find the exact value of the six trig functions of
?
Hint First find the length of the hypotenuse
using the Pythagorean Theorem.
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Example (cont)

So the six trig functions are
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Example
Given that ? is an acute angle and
, find the exact value of the six trig
functions of ?.

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This is known as a Pythagorean Identity.
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Divide each side by cos2? to derive 2nd
Pythagorean Identity.
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Divide each side by sin2? to derive 3rd
Pythagorean Identity.
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• End of Section 7.2