Math  /  Trigonometry

QuestionIf θ=π9\theta=\frac{\pi}{9} radians, what is the value of θ\theta in degrees?

Studdy Solution

STEP 1

1. We are given an angle θ\theta in radians.
2. We need to convert this angle from radians to degrees.
3. The conversion factor between radians and degrees is 180=π radians180^\circ = \pi \text{ radians}.

STEP 2

1. Use the conversion factor to set up the equation.
2. Solve for θ\theta in degrees.

STEP 3

To convert radians to degrees, use the conversion factor 180=π radians180^\circ = \pi \text{ radians}. Set up the equation:
θdegrees=θradians×(180π)\theta_{\text{degrees}} = \theta_{\text{radians}} \times \left(\frac{180^\circ}{\pi}\right)
Substitute θ=π9\theta = \frac{\pi}{9} into the equation:
θdegrees=π9×(180π)\theta_{\text{degrees}} = \frac{\pi}{9} \times \left(\frac{180^\circ}{\pi}\right)

STEP 4

Simplify the equation by canceling π\pi in the numerator and denominator:
θdegrees=1809\theta_{\text{degrees}} = \frac{180^\circ}{9}
Calculate the division:
θdegrees=20\theta_{\text{degrees}} = 20^\circ
The value of θ\theta in degrees is:
20\boxed{20^\circ}

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