Pre-Calc Exam Notes 88

Pre-Calc Exam Notes 88 - Degrees Radians Degrees Radians...

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88 Chapter 4 Radian Measure §4.1 Formula (4.2) follows by dividing both sides of equation (4.1) by 360, so that 1 = 2 π 360 = π 180 radians, then multiplying both sides by x . Formula (4.3) is similarly derived by dividing both sides of equation (4.1) by 2 π then multiplying both sides by x . The statement θ = 2 π radians is usually abbreviated as θ = 2 π rad, or just θ = 2 π when it is clear that we are using radians. When an angle is given as some multiple of π , you can assume that the units being used are radians. Example 4.1 Convert 18 to radians. Solution: Using the conversion formula (4.2) for degrees to radians, we get 18 = π 180 · 18 = π 10 rad . Example 4.2 Convert π 9 radians to degrees. Solution: Using the conversion formula (4.3) for radians to degrees, we get π 9 rad = 180 π · π 9 = 20 . Table 4.1 Commonly used angles in radians
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Unformatted text preview: Degrees Radians Degrees Radians Degrees Radians Degrees Radians ◦ 90 ◦ π 2 180 ◦ π 270 ◦ 3 π 2 30 ◦ π 6 120 ◦ 2 π 3 210 ◦ 7 π 6 300 ◦ 5 π 3 45 ◦ π 4 135 ◦ 3 π 4 225 ◦ 5 π 4 315 ◦ 7 π 4 60 ◦ π 3 150 ◦ 5 π 6 240 ◦ 4 π 3 330 ◦ 11 π 6 O r r θ θ = 1 radian Figure 4.1.2 Table 4.1 shows the conversion between degrees and radians for some common angles. Using the conversion formula (4.3) for radians to degrees, we see that 1 radian = 180 π degrees ≈ 57.3 ◦ . Formally, a radian is de±ned as the central angle in a circle of radius r which intercepts an arc of length r , as in Figure 4.1.2. This de±nition does not depend on the choice of r (imagine resizing Figure 4.1.2)....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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