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Trig Functions Review (Including Trig Quiz Solutions)

Trig Functions Review (Including Trig Quiz Solutions). MHF4UI Friday November 16 th , 2012. Convert the following angles to Radians. Provide Exact Answers. Convert the following angles to Degrees. Round to the nearest degree. Question 3: Finding the Arc Length.

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Trig Functions Review (Including Trig Quiz Solutions)

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  1. Trig Functions Review(Including Trig Quiz Solutions) MHF4UI Friday November 16th, 2012

  2. Convert the following angles to Radians. Provide Exact Answers

  3. Convert the following angles to Degrees. Round to the nearest degree.

  4. Question 3: Finding the Arc Length Therefore he travelled a distance of about 86.39 metres. Therefore his angular velocity is per minute.

  5. Question 6: Solve the Equation

  6. Why must we have In a right angled triangle, the absolute value of the length of the hyp will always be greater than or equal to absolute value of the length of the adj Therefore

  7. What is a Radian? Much like a degree, a Radian is a measurement of an angle. The radian measure of an angle ,ϴ, is defined as the length, a, of the arc that “subtends” the angle divided by the radius of the arc ,r

  8. Radian Relationship to Degrees

  9. Word Problems

  10. Trig Ratios Within a right angled triangle we will have that:

  11. Finding Trig Ratios We found Trig Ratios using our Related Acute angles of: We found trig ratios by drawing our angles in standard position. We found trig ratios when our terminal arm lies on the x or y axis. We also used trig ratios to solve word problems (Kite Example)

  12. Solving Trig Equations We solved for simple trig equations by using our special acute angles. We solved for trig equations by using our trig inverse function and finding We also encountered cases where we had to rearrange our equation and isolate our trig function. We used factoring or the quadratic formula to solve trig equations. When we solved Trig Equations we must note the restriction on our solution: - • No restrictions (infinite solutions) • - other restrictions (we added or subtracted )

  13. Graphing Trig Functions We sketched the graphs of all 6 trig functions We found the characteristics of each of these trig functions: • Max/Min • Amplitude • Period • Intercepts • Asymptotes

  14. Transformations of Sinusoidal Functions The general form of a Sinusoidal Function can be written as: OR We discussed the effects of variables a, k, c and d on the function We used mapping notation to graph our transformed functions We found the 5 key points for both sine and cosine functions We also used formulas of amplitude, period, vertical shift as well as our knowledge of the behaviour of sine and cosine functions to find the equation in general form

  15. Applications of Sinusoidal Functions We applied sine and cosine functions to real life scenarios where we: • Sketched the function • Found the characteristics of the function • Found the equation of the function that would model the scenario • Solved for specific values of the function

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