8) [tex]\theta[/tex] is -0.896 radians
9) length of arc is 41.91 cm
Solution:
8)
Given that,
[tex]tan\ \theta = \frac{-5}{4}[/tex]
[tex]\theta[/tex] is in quadrant 4
To find: [tex]\theta[/tex]
From given,
[tex]tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34[/tex]
Thus value of [tex]\theta[/tex] is -51.34 degrees
Convert degrees to radians
[tex]-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian[/tex]
Thus [tex]\theta[/tex] is -0.896 radians
9)
From given,
radius = 15.4 cm
[tex]\theta = \frac{13 \pi }{15}[/tex]
The length of arc when angle in radians is:
[tex]arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91[/tex]
Thus length of arc is 41.91 cm
