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 θ = 32 ◦ . Find the angle between 0 ◦ and 360 ◦ which is the (a) reflection of θ around the x-axis (b) reflection of θ around the y-axis (c) reflection of θ around the origin 2. Repeat Exercise 1 with θ = 248 ◦ . 3. Repeat Exercise 1 with θ =− 248 ◦ . 4. We proved formulas (1.4)-(1.6) for any angle θ in QI. Mimic that proof to show that the formulas hold for θ in QII. 5. Verify formulas (1.4)-(1.6) for θ on the coordinate axes, i.e. for θ = ◦ , 90 ◦ , 180 ◦ , 270 ◦ . 6. In Example 1.26 we used the formulas involving θ + 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 θ − 90 ◦ . ( Hint: Only the last paragraph in that example needs to be modified. ) For Exercises 7 - 14, find all angles 0 ◦ ≤ θ < 360 ◦ which satisfy the given equation: 7. sin θ = 0.4226 8. sin θ = 0.19090....
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