Coterminal Angles

Coterminal angles are angles that share the same initial side and terminal side. In degrees, coterminal angles differ by multiples of \(360^\circ\), and in radians, they differ by multiples of \(2\pi\). These problems practice finding positive and negative coterminal angles in both degree and radian measure.

Notes

Notes for Coterminal Angles

 

Practice Problems

Find 2 coterminal angles (one positive and one negative)

\(\textbf{1)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=100^{\circ}\) Link to Youtube Video Solving Question Number 1

 

\(\textbf{2)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=641^{\circ}\) Link to Youtube Video Solving Question Number 2

 

\(\textbf{3)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=-281^{\circ}\)Link to Youtube Video Solving Question Number 3

 

\(\textbf{4)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=40^{\circ}\)

 

\(\textbf{5)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{\pi}{3}\)

 

\(\textbf{6)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{3\pi}{4}\)

 

\(\textbf{7)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{7\pi}{15}\)

 

\(\textbf{8)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{\pi}{7}\)

 

\(\textbf{9)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=215^{\circ}\)

 

\(\textbf{10)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=-150^{\circ}\)

 

\(\textbf{11)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=330^{\circ}\)

 

\(\textbf{12)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{5\pi}{6}\)

 

\(\textbf{13)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{2\pi}{5}\)

 

\(\textbf{14)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{11\pi}{9}\)

 

\(\textbf{15)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{4\pi}{11}\)

 

Challenge Problems

\(\textbf{16)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{9\pi}{8}\)

 

\(\textbf{17)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=-725^\circ\)

 

\(\textbf{18)}\) Find 2 coterminal angles (one positive and one negative)
\(\theta=1080^\circ\)

 

\(\textbf{19)}\) Find 2 coterminal angles (one positive and one negative)
\(x=-\displaystyle\frac{13\pi}{6}\)

 

\(\textbf{20)}\) Find 2 coterminal angles (one positive and one negative)
\(x=\displaystyle\frac{17\pi}{10}\)

 

 

See Related Pages\(\)

\(\bullet\text{ Right Triangle Trigonometry}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\)
\(\bullet\text{ Angle of Depression and Elevation}\)
\(\,\,\,\,\,\,\,\,\text{Angle of Depression}=\text{Angle of Elevation}…\)
\(\bullet\text{ Convert to Radians and to Degrees}\)
\(\,\,\,\,\,\,\,\,\text{Radians} \rightarrow \text{Degrees}, \times \displaystyle \frac{180^{\circ}}{\pi}…\)
\(\bullet\text{ Degrees, Minutes and Seconds}\)
\(\,\,\,\,\,\,\,\,48^{\circ}34’21”…\)
\(\bullet\text{ Coterminal Angles}\)
\(\,\,\,\,\,\,\,\,\pm 360^{\circ} \text { or } \pm 2\pi n…\)
\(\bullet\text{ Reference Angles}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Reference Angles\(…\)
\(\bullet\text{ Find All 6 Trig Functions}\)
\(\,\,\,\,\,\,\,\,\)Thumbnail for Find 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\(…\)
\(\bullet\text{ Solving Trigonometric Equations}\)
\(\,\,\,\,\,\,\,\,2\cos{(x)}=\sqrt{3}…\)

 

Scroll to Top