Mat 161 PreCalculus

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Mat 161 - PreCalculus

• More Trigonometric Properties
• Section 7.1

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More Unit Circle Trigonometry

• Def Let P (x, y) be a point on the unit
  circle that has arc length t from (1,0), then we
  define the six trigonometric functions of t as
  follows
• sin(t) y csc(t) 1/y
• cos(t) x sec(t) 1/x
• tan (t) y/x cot(t) x/y

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Unit Circle Trigonometry

• Observations/Identities
• 1) sin2t cos2t 1 5) sec t 1/cos t
• 2) tan2t 1 sec2t 6) cot t 1/tan t
• 3) 1 cot2t csc2t 7) tan t sint/cost
• 4) csct 1/sint 8) cot t
  cost/sint

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More Trigonometric Properties

• Observations/Identities Cont.
• sin(-t) -sin(t)
• cos(-t) cos(t)
• tan(-t) -tan(t)
• sin(t k2p) sin(t)
• cos(t k2p) cos(t)
• tan(t kp) tan(t)

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More Trigonometric Properties

• Use the above observations to find the
  following
• a) sin ( -45º)
• b) cos (-60º)
• c) sin(390º)
• d) cos(-240º)
• e) tan ( -p/6)
• f) tan(7p/6)

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More Trigonometric PropertiesSection 7.1

• Reference
• Cohen
• PreCalculus
• 4th Edition