1 Answer

Mainajaved · Answer 1 · 2021-01-11T19:01:22+0000

8)
$\theta$ is -0.896 radians

9) length of arc is 41.91 cm

Solution:

8)

Given that,

$tan\ \theta = (-5)/(4)$

$\theta$ is in quadrant 4

To find:
$\theta$

From given,

$tan\ \theta = (-5)/(4)\\\\\theta = tan^(-1) (-5)/(4)\\\\\theta = tan^(-1) (-1.25)\\\\\theta = -51.34$

Thus value of
$\theta$ is -51.34 degrees

Convert degrees to radians

$-51.34\ degree = -51.34 * ( \pi )/(180)\ radian\\\\-51.34\ degree = -0.896\ radian$

Thus
$\theta$ is -0.896 radians

9)

From given,

radius = 15.4 cm

$\theta = (13 \pi )/(15)$

The length of arc when angle in radians is:

$arc\ length = r * \theta\\\\arc\ length = 15.4 * ( 13 \pi )/(15)\\\\arc\ length = 15.4 * 2.721\\\\arc\ length = 41.91$

Thus length of arc is 41.91 cm

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