Mat 152 - Trigonometry

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Mat 152 - Trigonometry

• Algebra and the Trigonometric Functions
• Section 6.4

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Section 6.4 Algebra and the Trigonometric
Functions

• In order to evaluate the trigonometric
  functions of angles/numbers we may also be able
  use the identities. So, lets recall the Basic
  Identities we have observed from the definition

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Section 6.4 Algebra and the Trigonometric
Functions

• Observations/Identities
• sin2? cos2? 1
• 2) tan2? 1 sec2?
• 3) 1 cot2? csc2?
• 4) csc? 1/sin?
• 5) sec? 1/cos?
• 6) cot? 1/tan?
• 7) tan? sin?/cos?
• 8) cot? cos?/sin?

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Section 6.4 Algebra and the Trigonometric
Functions

• Evaluate the trigonometric functions of
• an angle ? provided that we know that
• sin ? - 1/8 and that p lt ? lt 3p/2.

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Section 6.4 Algebra and the Trigonometric
Functions

• Evaluate the trigonometric functions of
• an angle ? provided that we know that
• tan ? -4 and that 3p/2 lt ? lt 2p.

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Section 6.4 Algebra and the Trigonometric
Functions

• In addition to computing trigonometric
• functions of angles, we are also able to
• manipulate expressions involving
• trigonometric expressions in them. We
• may also want to construct new identities
• or even prove them.

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Section 6.4 Algebra and the Trigonometric
Functions

• Prove the following identities.
• cosx cscx cotx
• cotx secx sinx 1
• cos2x sin2x 2cos2x - 1

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Prove the following Identities
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Section 6.4 Algebra and the Trigonometric
Functions

• Reference
• PreCalculus
• Cohen
• 4th Edition