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Understanding Inverse Trig Functions

Learn how to find angle measures for given trig function values using sine-1, cosine-1, and tangent-1. Discover the restrictions and intervals for each function.

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Understanding Inverse Trig Functions

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  1. Chapter 7 Analytic Trigonometry

  2. Section 1The Inverse Sine, Cosine, and Tangent Functions

  3. Previously, the questions were written as: sin cos tan Which meant go to the given angle measure on the unit circle and evaluate the given trig function The answer would have been some sort of variation of the ordered pair listed at the angle

  4. Now the questions will be presented as: sin-1x cos-1x tan-1x Which means they are telling you the given trig function would give you a value of x, what angle does this happen at The answer should be an angle measure from the unit circle in RADIANS The catch: what does is mean to be a function?  every x can only have ONE answer!

  5. Example: Find sin-1(1/2) Think: where on the unit circle would sin = ½? Happens at __________ and __________ However…. (continued on next slide)

  6. In order for sin-1, cos-1, and tan-1 to be defined as functions, they have restrictions on which quadrants they can exist in. All Students Take Calculus

  7. We need to have a continuous interval on which we can get every possible answer but no repeats.

  8. cos-1x is the easiest only exists in quadrants I and II and the answers can only be given in the interval of 0 ≤ ≤ sin-1x and tan-1x only exists in quadrants I and IV and the answers can only be given in the intervals of: sin-1x: -/2 ≤ ≤ /2 tan-1x: -/2 < < /2

  9. **meaning in the 4th quadrant, your answers are given as how far you moved from zero: On the unit circle Inverse answers

  10. So… Now when the question sin-1(1/2) is asked, the only answer should be ________. Find: cos-1() tan-1(1)

  11. Example: sin-1[sin(-/3)] = -/3 ? cos[cos-1(3)] = 3 ? cos-1[cos(-/3)] = -/3?

  12. EXIT SLIP

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