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Pre-Calc Exam Notes 36

Pre-Calc Exam Notes 36 - 36 Chapter 1 Right Triangle...

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36 Chapter 1 Right Triangle Trigonometry §1.5 Notice that reflection around the y -axis is equivalent to reflection around the x -axis ( θ mapstochar→ θ ) followed by a rotation of 180 ( θ mapstochar→− θ + 180 = 180 θ ), as in Figure 1.5.7. x y θ θ r r ( x , y ) ( x , y ) ( x , y ) 180 θ r Figure 1.5.7 Reflection of θ around the y -axis = 180 θ It may seem that these geometrical operations and formulas are not necessary for evalu- ating the trigonometric functions, since we could just use a calculator. However, there are two reasons for why they are useful. First, the formulas work for any angles, so they are often used to prove general formulas in mathematics and other fields, as we will see later in the text. Second, they can help in determining which angles have a given trigonometric function value. Example1.27 Find all angles 0 θ < 360 such that sin θ =− 0 . 682. Solution: Using the a0 sin 1 button on a calculator with
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