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6.3.1 Trigonometric Functions of Real Numbers

6.3.1 Trigonometric Functions of Real Numbers. Radians vs. Real Numbers. The argument of a trig function can be a real number, radians, or degrees. Sin(2) real number, radian, or degree? Sin(2 ) real number, radian, or degree? Note: sin(2) ≠ sin(2). Unit Circle.

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6.3.1 Trigonometric Functions of Real Numbers

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  1. 6.3.1 Trigonometric Functions of Real Numbers

  2. Radians vs. Real Numbers • The argument of a trig function can be a real number, radians, or degrees. • Sin(2) real number, radian, or degree? • Sin(2) real number, radian, or degree? • Note: • sin(2) ≠ sin(2)

  3. Unit Circle • The unit circle defines the trig functions in terms of the dependent variable • If we consider time in radians as our x-values we can consider the yt plane (similar to xy plane except t values for x axis)

  4. sin(t) = y cos(t) = x tan(t) = csc(t) = sec(t) = cot(t) = Functions definedP(x,y) on the unit circle

  5. Since these functions are defined by a circle… • On a circle 180 or half a circle or  • Produces a t-value of exact opposite value • Similarly 360 or a whole circle or 2 • Produces a t-value of the same value

  6. This defines our functions as follows: • P(t) = (x, y) • P(t + ) = (-x, -y) • P(t - ) = (-x, -y) • P(-t) = (x, -y)

  7. Given, Since P(-t - ) = P(-(t + )) Find P(t +  ), P(t -  ), P(-t), and P(-t - ) P(-t - ) P(t) P(-t) P(t + ), P(t - )

  8. Remember! • P(x,y) = P(cos(t) , sin(t)) • Where t is the angle in radians

  9. 10)a) - sin(-)= 0 cos(-)= -1 tan(-)= 0 csc(-)= U sec(-)= -1 cot(-)= U Find the Values of the Trigonometric Fucntions  0 (2) (-1, 0)

  10. 10)b) 6 sin(6)= cos(6)= tan(6)= csc(6)= sec(6)= cot(6)= You Try!  0 (2)

  11. Homework • p. 436 1-4, 5-8, 9-15 odd

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