Question

Convert the angle \theta=\dfrac{17\pi}{18}θ= 18 17π ​ theta, equals, start fraction, 17, pi, divided by, 18, end fraction radians to degrees. Express your answer exactly. \theta=θ=theta, equals ^\circ ∘

Answer 1

Answer:

θ = 170°

Step-by-step explanation:

Given angle is in radian as,

$\theta^{c} = \dfrac{17 \pi}{18}$

Here, $\theta^{c}$ symbol represents the angle is in radian.

To convert given angle into degree, multiply the given angle with conversion factor as follows,

$\theta^{\circ} = \theta^{c} \times \left(\frac{180}{\pi }\right)^{\circ}$

Substituting the values,

$\theta^{\circ} =  \dfrac{17 \pi}{18} \times \left(\dfrac{180}{\pi }\right)$

Cancelling out the common terms,

$\theta^{\circ} =17\times \left(10\right)$

Therefore,

$\theta^{\circ} =170^{\circ}$

Therefore the value of given angle in degree is 170°