Exercise 79 Page 456

Half a lap around the unit circle equals 180^(∘) and an arc length of π. 180^(∘) = π If we manipulate this equation until the left-hand side equals the different angles from the table, we can determine the corresponding number of radians.

c|c|l θ & θ * x = π & Solve for θ [-0.5em] 45^(∘) & 45^(∘) * 4=π & 45^(∘) =π/4 [0.8em] [-0.5em] 60^(∘) & 60^(∘) * 3=π & 60^(∘) =π/3 [0.8em] [-0.5em] 90^(∘) & 90^(∘) * 2=π & 90^(∘) =π/2 [0.8em] [-0.5em] 120^(∘) & 120^(∘) * 3/2=π & 120^(∘)=2π/3 [0.8em] [-0.5em] 135^(∘) & 135^(∘) * 4/3=π & 135^(∘)=3π/4 [0.8em] [-0.5em] 150^(∘) & 150^(∘) * 6/5=π & 150^(∘)=5π/6 [0.8em] [-0.5em] 180^(∘) & 180^(∘) * 1=π & 180^(∘)=π [0.8em] [-0.5em] 210^(∘) & 210^(∘) * 6/7=π & 210^(∘)=7π/6 [0.8em] [-0.5em] 225^(∘) & 225^(∘) * 4/5=π & 225^(∘)=5π/4 [0.8em] [-0.5em] 240^(∘) & 240^(∘) * 3/4=π & 240^(∘)=4π/3 [0.8em] [-0.5em] 270^(∘) & 270^(∘) * 2/3=π & 270^(∘)=3π/2 [0.8em] [-0.5em] 300^(∘) & 300^(∘) * 3/5=π & 300^(∘)=5π/3 [0.8em] [-0.5em] 315^(∘) & 315^(∘) * 4/7=π & 315^(∘)=7π/4 [0.8em] [-0.5em] 330^(∘) & 330^(∘) * 6/11=π & 330^(∘)=11π/6 [0.8em] Now we can fill out the table. c|c|c|c|c|c Degrees & 0 & 30 & 45 & 60 & 90 [0.2em] [-0.5em] Radians & 0 & π/6 & π/4 & π/3 & π/2 c|c|c|c|c|c Degrees & 120 & 135 & 150 & 180 & 210 [0.2em] [-0.5em] Radians & 2π/3 & 3π/4 & 5π/6 & π & 7π/6 c|c|c|c|c|c|c Degrees & 225 & 240 & 270 & 300 & 315 & 330 [0.2em] [-0.5em] Radians & 5π/4 & 4π/3 & 3π/2 & 5π/3 & 7π/4 & 11π/6

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