Degrees, minutes, and seconds form is a way to write angle measures using smaller parts of a degree. One degree is split into \(60\) minutes, and one minute is split into \(60\) seconds. These problems practice converting between decimal degrees and D°M’S” form, as well as finding reference angles written with degrees and minutes.
Lesson
Notes
Converting from D°M’S” form to Decimal Form
\(\hspace{25pt}\text{D°M’S”}=D+\displaystyle\frac{M}{60}+\displaystyle\frac{S}{3600}^{\circ}\)
Practice Problems
Convert from D°M’S” form to Decimal Form
\(\textbf{1)}\) \(14^{\circ}\,22{‘}\,17{‘}{‘}\)
\(\textbf{2)}\) \(160^{\circ}\,56{‘}\,12{‘}{‘}\)
\(\textbf{3)}\) \(12^{\circ}\,35{‘}\,19{‘}{‘}\)
\(\textbf{4)}\) \(90^{\circ}\,42{‘}\,37{‘}{‘}\)
Convert from decimal form to D°M’S” Form
\(\textbf{5)}\) \(18.45^{\circ}\)
\(\textbf{6)}\) \(157.82^{\circ}\)
\(\textbf{7)}\) \(130.63^{\circ}\)
\(\textbf{8)}\) \(56.896^{\circ}\)
Find the reference angle for the following
\(\textbf{9)}\) \( 154^{\circ} 49′ \)
\(\textbf{10)}\) Convert \(48^{\circ}\,34{‘}\,21{‘}{‘}\) to decimal form.
\(\textbf{11)}\) Convert \(225^{\circ}\,15{‘}\,30{‘}{‘}\) to decimal form.
\(\textbf{12)}\) Convert \(42.375^\circ\) to D°M’S” form.
\(\textbf{13)}\) Convert \(73.125^\circ\) to D°M’S” form.
\(\textbf{14)}\) Convert \(112.256^\circ\) to D°M’S” form.
\(\textbf{15)}\) Find the reference angle for \(215^\circ30′\).
Challenge Problems
\(\textbf{16)}\) Find the reference angle for \(322^\circ18′\).
\(\textbf{17)}\) Convert \(359^\circ\,59{‘}\,30{‘}{‘}\) to decimal form.
\(\textbf{18)}\) Convert \(12.999^\circ\) to D°M’S” form.
\(\textbf{19)}\) Find the reference angle for \(278^\circ42′\).
\(\textbf{20)}\) Convert \(24^\circ\,37{‘}\,12{‘}{‘}\) to decimal form.
See Related Pages\(\)
\(\bullet\text{ Right Triangle Trigonometry}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\)
\(\bullet\text{ Angle of Depression and Elevation}\)
\(\,\,\,\,\,\,\,\,\text{Angle of Depression}=\text{Angle of Elevation}…\)
\(\bullet\text{ Convert to Radians and to Degrees}\)
\(\,\,\,\,\,\,\,\,\text{Radians} \rightarrow \text{Degrees}, \times \displaystyle \frac{180^{\circ}}{\pi}…\)
\(\bullet\text{ Degrees, Minutes and Seconds}\)
\(\,\,\,\,\,\,\,\,48^{\circ}34’21”…\)
\(\bullet\text{ Coterminal Angles}\)
\(\,\,\,\,\,\,\,\,\pm 360^{\circ} \text { or } \pm 2\pi n…\)
\(\bullet\text{ Reference Angles}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Find All 6 Trig Functions}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Unit Circle}\)
\(\,\,\,\,\,\,\,\,\sin{(60^{\circ})}=\displaystyle\frac{\sqrt{3}}{2}…\)
\(\bullet\text{ Law of Sines}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}\) 
\(…\)
\(\bullet\text{ Area of SAS Triangles}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\frac{1}{2}ab \sin{C}\) \(…\)
\(\bullet\text{ Law of Cosines}\)
\(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{A}\) \(…\)
\(\bullet\text{ Area of SSS Triangles (Heron’s formula)}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\) \(…\)
\(\bullet\text{ Geometric Mean}\)
\(\,\,\,\,\,\,\,\,x=\sqrt{ab} \text{ or } \displaystyle\frac{a}{x}=\frac{x}{b}…\)
\(\bullet\text{ Geometric Mean- Similar Right Triangles}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Inverse Trigonmetric Functions}\)
\(\,\,\,\,\,\,\,\,\sin {\left(cos^{-1}\left(\frac{3}{5}\right)\right)}…\)
\(\bullet\text{ Sum and Difference of Angles Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(A+B)}=\sin{A}\cos{B}+\cos{A}\sin{B}…\)
\(\bullet\text{ Double-Angle and Half-Angle Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(2A)}=2\sin{(A)}\cos{(A)}…\)
\(\bullet\text{ Trigonometry-Pythagorean Identities}\)
\(\,\,\,\,\,\,\,\,\sin^2{(x)}+\cos^2{(x)}=1…\)
\(\bullet\text{ Product-Sum Identities}\)
\(\,\,\,\,\,\,\,\,\cos{\alpha}\cos{\beta}=\left(\displaystyle\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\right)…\)
\(\bullet\text{ Cofunction Identities}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\cos{(\frac{\pi}{2}-x)}…\)
\(\bullet\text{ Proving Trigonometric Identities}\)
\(\,\,\,\,\,\,\,\,\sec{x}-\cos{x}=\displaystyle\frac{\tan^2{x}}{\sec{x}}…\)
\(\bullet\text{ Graphing Trig Functions- sin and cos}\)
\(\,\,\,\,\,\,\,\,f(x)=A \sin{B(x-c)}+D \) 
\(…\)
\(\bullet\text{ Solving Trigonometric Equations}\)
\(\,\,\,\,\,\,\,\,2\cos{(x)}=\sqrt{3}…\)