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WARM UP

WARM UP. Determine two coterminal angles (in degrees) for 114 ° Find (if possible) the complement and supplement of 36° Convert 315° to radians Convert 7 π /3 to degrees Convert 310.75 ° to D°M'S". 4.2 The Unit Circle. Here It Is…. sin t = y cos t = x tan t = y / x.

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WARM UP

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  1. WARM UP • Determine two coterminal angles (in degrees) for 114° • Find (if possible) the complement and supplement of 36° • Convert 315° to radians • Convert 7π/3 to degrees • Convert 310.75° to D°M'S"

  2. 4.2The Unit Circle

  3. Here It Is…

  4. sin t = y cos t = x tan t = y/x csc t = 1/sin t = 1/y sec t = 1/cos t = 1/x cot t = 1/ tan t = x/y There are 6 Trigonometric Functions Let t be a real number and (x, y) be the point on the unit circle corresponding to t.

  5. Examples Evaluate the six trig functions for each: • t = π/6 • t = 5π/4

  6. Answers

  7. Evaluate sin 13π/6 using its period as an aid. Because 13π/6 = 2π + π/6 it follows that… sin 13π/6 is the same as π/6 which is equal to ½. Therefore sin 13π/6 = ½

  8. Even and Odd Trig Functions • The cosine and secant functions are even. • cos (-t) = cos t sec (-t) = sec t • The sine, cosecant, tanget and cotangent are odd • sin (-t) = - sin t csc (-t) = - csc t • tan (-t) = - tan t cot (-t) = - cot t • **This is true because of the rules from chapter 1 that say if f(-x) = f(x) then it is even. And if f(-x) = -f(x), then it is odd.

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