Question

Convert the angle \theta=\dfrac{8\pi}{9}θ=

9
8π
​
theta, equals, start fraction, 8, pi, divided by, 9, end fraction radians to degrees.

Answer 1

`160^\circ` is the degrees value of
`\theta = (8 \pi)/(9)`.

Explanation:

We are given the following details about the angle
`\theta`:

`\theta =(8\pi)/(9)\text{ radians}`

It is know that the relation between radians and degree units is as follows:

`\pi \text{ radians} = 180 ^\circ`

We can use simply use unitary method to convert radian value of
`\theta` to degrees.

`\pi \text{ radians} = 180 ^\circ`

`\Rightarrow 1 \text { radian}= (\pi)/(180) ^\circ`

`\Rightarrow (8\pi)/(9) \text{ radians} = (180)/(\pi) * (8\pi)/(9) ^\circ\\\Rightarrow (180 * 8)/(9)^\circ\\\Rightarrow 20 * 8^\circ\\\Rightarrow 160 ^\circ`

Hence,
`\theta = 160^\circ`