Convert to Radians and to Degrees

Converting between degrees and radians is an important skill for working with angles in trigonometry and the unit circle. To convert degrees to radians, multiply by \(\frac{\pi}{180^\circ}\), and to convert radians to degrees, multiply by \(\frac{180^\circ}{\pi}\). These problems practice both directions, including positive angles, negative angles, improper radian measures, and common unit-circle angles.

Notes

Notes for Converting

Practice Problems

\(\textbf{1)}\) Convert \( \theta=55^{\circ} \) from degrees to radiansLink to Youtube Video Solving Question Number 1

 

\(\textbf{2)}\) Convert \( \theta=270^{\circ} \) from degrees to radians

 

\(\textbf{3)}\) Convert \( \theta=-275^{\circ} \) from degrees to radians

 

\(\textbf{4)}\) Convert \( \theta=140^{\circ} \) from degrees to radians

 

\(\textbf{5)}\) Convert \( \theta=-36^{\circ} \) from degrees to radians

 

\(\textbf{6)}\) Convert \( \theta=400^{\circ} \) from degrees to radians

 

\(\textbf{7)}\) Convert \( x=\displaystyle\frac{-7\pi}{5} \) from radians to degreesLink to Youtube Video Solving Question Number 7

 

\(\textbf{8)}\) Convert \( x=\displaystyle\frac{-5\pi}{3} \) from radians to degrees

 

\(\textbf{9)}\) Convert \( x=\displaystyle\frac{4\pi}{5} \) from radians to degrees

 

\(\textbf{10)}\) Convert \( x=\displaystyle\frac{\pi}{8} \) from radians to degrees

 

\(\textbf{11)}\) Convert \( x=\displaystyle\frac{5\pi}{12} \) from radians to degrees

 

\(\textbf{12)}\) Convert \( \theta=315^{\circ} \) from degrees to radians

 

\(\textbf{13)}\) Convert \( \theta=225^{\circ} \) from degrees to radians

 

\(\textbf{14)}\) Convert \( \theta=-150^{\circ} \) from degrees to radians

 

\(\textbf{15)}\) Convert \( x=\displaystyle\frac{11\pi}{6} \) from radians to degrees

 

Challenge Problems

\(\textbf{16)}\) Convert \( x=-\displaystyle\frac{13\pi}{4} \) from radians to degrees

 

\(\textbf{17)}\) Convert \( \theta=765^{\circ} \) from degrees to radians

 

\(\textbf{18)}\) Convert \( x=\displaystyle\frac{19\pi}{10} \) from radians to degrees

 

\(\textbf{19)}\) Convert \( \theta=-720^{\circ} \) from degrees to radians

 

\(\textbf{20)}\) Convert \( x=-\displaystyle\frac{17\pi}{12} \) from radians to degrees

 

 

See Related Pages\(\)

\(\bullet\text{ Visualizing Radians}\)
\(\,\,\,\,\,\,\,\,\text{(Geogebra.org)}\)
\(\bullet\text{ Right Triangle Trigonometry}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\)
\(\bullet\text{ Angle of Depression and Elevation}\)
\(\,\,\,\,\,\,\,\,\text{Angle of Depression}=\text{Angle of Elevation}…\)
\(\bullet\text{ Convert to Radians and to Degrees}\)
\(\,\,\,\,\,\,\,\,\text{Radians} \rightarrow \text{Degrees}, \times \displaystyle \frac{180^{\circ}}{\pi}…\)
\(\bullet\text{ Degrees, Minutes and Seconds}\)
\(\,\,\,\,\,\,\,\,48^{\circ}34’21”…\)
\(\bullet\text{ Coterminal Angles}\)
\(\,\,\,\,\,\,\,\,\pm 360^{\circ} \text { or } \pm 2\pi n…\)
\(\bullet\text{ Reference Angles}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail of Reference Angles\(…\)
\(\bullet\text{ Find All 6 Trig Functions}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail of all 6 Trig Functions\(…\)
\(\bullet\text{ Unit Circle}\)
\(\,\,\,\,\,\,\,\,\sin{(60^{\circ})}=\displaystyle\frac{\sqrt{3}}{2}…\)
\(\bullet\text{ Law of Sines}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}\) Thumbnail for Law of Sines\(…\)
\(\bullet\text{ Area of SAS Triangles}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\frac{1}{2}ab \sin{C}\) Thumbnail for Area of SAS Triangles\(…\)
\(\bullet\text{ Law of Cosines}\)
\(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{A}\) Thumbnail for Law of Cosines\(…\)
\(\bullet\text{ Area of SSS Triangles (Heron’s formula)}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\) Thumbnail for Heron's Formula\(…\)
\(\bullet\text{ Geometric Mean}\)
\(\,\,\,\,\,\,\,\,x=\sqrt{ab} \text{ or } \displaystyle\frac{a}{x}=\frac{x}{b}…\)
\(\bullet\text{ Geometric Mean- Similar Right Triangles}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Similar Right Triangles\(…\)
\(\bullet\text{ Inverse Trigonmetric Functions}\)
\(\,\,\,\,\,\,\,\,\sin {\left(cos^{-1}\left(\frac{3}{5}\right)\right)}…\)
\(\bullet\text{ Sum and Difference of Angles Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(A+B)}=\sin{A}\cos{B}+\cos{A}\sin{B}…\)
\(\bullet\text{ Double-Angle and Half-Angle Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(2A)}=2\sin{(A)}\cos{(A)}…\)
\(\bullet\text{ Trigonometry-Pythagorean Identities}\)
\(\,\,\,\,\,\,\,\,\sin^2{(x)}+\cos^2{(x)}=1…\)
\(\bullet\text{ Product-Sum Identities}\)
\(\,\,\,\,\,\,\,\,\cos{\alpha}\cos{\beta}=\left(\displaystyle\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\right)…\)
\(\bullet\text{ Cofunction Identities}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\cos{(\frac{\pi}{2}-x)}…\)
\(\bullet\text{ Proving Trigonometric Identities}\)
\(\,\,\,\,\,\,\,\,\sec{x}-\cos{x}=\displaystyle\frac{\tan^2{x}}{\sec{x}}…\)
\(\bullet\text{ Graphing Trig Functions- sin and cos}\)
\(\,\,\,\,\,\,\,\,f(x)=A \sin{B(x-c)}+D \) Thumbnail for Graphing Trig Functions\(…\)
\(\bullet\text{ Solving Trigonometric Equations}\)
\(\,\,\,\,\,\,\,\,2\cos{(x)}=\sqrt{3}…\)

 

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