Question 4.1.1: Computing Radian Measure A central angle, θ, in a circle of ...

Computing Radian Measure

A central angle, θ, in a circle of radius 6 inches intercepts an arc of length 15 inches. What is the radian measure of θ ?

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Angle θ is shown in Figure 4.8. The radian measure of a central angle is the length of the intercepted arc, s, divided by the circle’s radius, r. The length of the intercepted arc is 15 inches: s = 15 inches. The circle’s radius is 6 inches: r = 6 inches. Now we use the formula for radian measure to find the radian measure of θ.

$\theta=\frac{s}{r}=\frac{15 \cancel{inches}}{6 \cancel{inches}}=2.5$

Thus, the radian measure of θ is 2.5.

4.8

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