Pre-Calc Exam Notes 37

Pre-Calc Exam Notes 37 - Rotations and Reflections of...

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Unformatted text preview: Rotations and Reflections of Angles Section 1.5 37 Exercises 1. Let = 32 . Find the angle between 0 and 360 which is the (a) reflection of around the x-axis (b) reflection of around the y-axis (c) reflection of around the origin 2. Repeat Exercise 1 with = 248 . 3. Repeat Exercise 1 with = 248 . 4. We proved formulas (1.4)-(1.6) for any angle in QI. Mimic that proof to show that the formulas hold for in QII. 5. Verify formulas (1.4)-(1.6) for on the coordinate axes, i.e. for = , 90 , 180 , 270 . 6. In Example 1.26 we used the formulas involving + 90 to prove that the slopes of perpendicu- lar lines are negative reciprocals. Show that this result can also be proved using the formulas involving 90 . ( Hint: Only the last paragraph in that example needs to be modified. ) For Exercises 7 - 14, find all angles 0 < 360 which satisfy the given equation: 7. sin = 0.4226 8. sin = 0.19090....
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