Convert from Degrees to Radians 290

Problem

${290}^{\circ }$

Solution

1. Identify the conversion factor between degrees and radians, which is $\frac{\pi \text{ radians}}{{180}^{\circ }}$

2. Multiply the given angle in degrees by this conversion factor to set up the expression.

${290}^{\circ }\cdot \frac{\pi }{{180}^{\circ }}$

3. Simplify the fraction by canceling the degree units and dividing both the numerator and denominator by their greatest common divisor, which is $10$

$\frac{290\pi }{180}$

4. Reduce the fraction $\frac{29}{18}$ to its simplest form. Since $29$ is a prime number and does not divide $18$ the fraction is already in simplest form.

$\frac{29\pi }{18}$

Final Answer

${290}^{\circ }=\frac{29\pi }{18}$

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