Convert the angle theta=(5pi)/(12) radians to degrees. Express your answer exactly. theta=◻" 。 "

Understanding radians and degrees: Understand the relationship between radians and degrees. One complete revolution around a circle is 2π radians or 360 degrees. Therefore, the conversion factor between radians and degrees is 180/π.Setting up the conversion formula: Set up the conversion from radians to degrees for theta. theta in degrees = theta in radians * (180/π)Substituting the given value: Substitute the given value of theta in radians into the conversion formula. theta in degrees = (5π/12) * (180/π)Simplifying the expression: Simplify the expression by multiplying the numerators and canceling out the π terms. theta in degrees = (5 * 180) / 12Calculating the final value: Divide 5 * 180 by 12 to find the value of theta in degrees. theta in degrees = 900 / 12Calculate the final value. theta in degrees = 75

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Convert the angle
theta=(5pi)/(12) radians to degrees.
Express your answer exactly.

theta=◻" 。 "

Convert the angle $\theta=\frac{5 \pi}{12}$ radians to degrees. $\newline$ Express your answer exactly. $\newline$ $\theta=\square^{\circ}$

View step-by-step help

Home

Math Problems

Precalculus

Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q. Convert the angle

\theta=\frac{5 \pi}{12}

radians to degrees.

\newline

Express your answer exactly.

\newline

\theta=\square^{\circ}

Understanding radians and degrees: Understand the relationship between radians and degrees. $\newline$ One complete revolution around a circle is $2\pi$ radians or $360$ degrees. Therefore, the conversion factor between radians and degrees is $\frac{180}{\pi}$ .
Setting up the conversion formula: Set up the conversion from radians to degrees for $\theta$ . $\theta \text{ in degrees} = \theta \text{ in radians} \times \left(\frac{180}{\pi}\right)$
Substituting the given value: Substitute the given value of $\theta$ in radians into the conversion formula. $\theta$ in degrees = $\left(\frac{5\pi}{12}\right) \times \left(\frac{180}{\pi}\right)$
Simplifying the expression: Simplify the expression by multiplying the numerators and canceling out the $\pi$ terms. $\theta$ in degrees = $\frac{5 \times 180}{12}$
Calculating the final value: Divide $5 \times 180$ by $12$ to find the value of $\theta$ in degrees. $\newline$ $\theta$ in degrees = $\frac{900}{12}$
Calculating the final value: Divide $5 \times 180$ by $12$ to find the value of $\theta$ in degrees. $\newline$ $\theta$ in degrees = $\frac{900}{12}$ Calculate the final value. $\newline$ $\theta$ in degrees = $75$