Practice Problems

Find all 6 trig functions

\(\textbf{1)}\) Find all 6 trig functions if \(\theta=180^{\circ}\)

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\(\sin⁡180^{\circ}=0\,\,\,\,\,\,\cos⁡180^{\circ}=-1\,\,\,\,\,\,\tan⁡180^{\circ}=0\)
\(\csc⁡180^{\circ}=\)undefined\(\,\,\,\,\,\,\sec⁡180^{\circ}=-1\,\,\,\,\,\,\cot⁡180^{\circ}=\)undefined

 

\(\textbf{2)}\) Find all 6 trig functions if \(\theta=330^{\circ}\)

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\(\sin⁡330^{\circ}=-\frac{1}{2}\,\,\,\,\,\,\cos⁡330^{\circ}=\frac{\sqrt{3}}{2}\,\,\,\,\,\,\tan⁡330^{\circ}=-\frac{\sqrt{3}}{3}\)
\(\csc⁡330^{\circ}=-2\,\,\,\,\,\,\sec⁡330^{\circ}=\frac{2\sqrt{3}}{3}\,\,\,\,\,\,\cot⁡330^{\circ}=-\sqrt{3}\)

 

\(\textbf{3)}\) Find all 6 trig functions if \(\theta=-135^{\circ}\)

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\(\sin⁡(-135^{\circ})=-\frac{\sqrt{2}}{2}\,\,\,\,\,\,\cos⁡(-135^{\circ})=-\frac{\sqrt{2}}{2}\,\,\,\,\,\,\tan⁡(-135^{\circ})=1\)
\(\csc⁡(-135^{\circ})=-\sqrt{2}\,\,\,\,\,\,\sec⁡(-135^{\circ})=-\sqrt{2}\,\,\,\,\,\,\cot⁡(-135^{\circ})=1\)

 

\(\textbf{4)}\) Find all 6 trig functions if the terminal side contains the point \((3,4)\)

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\(\sin⁡\theta=\frac{4}{5}\,\,\,\,\,\,\cos⁡\theta=\frac{3}{5}\,\,\,\,\,\,\tan⁡\theta=\frac{4}{3}\)
\(\csc⁡\theta=\frac{5}{4}\,\,\,\,\,\,\sec⁡\theta=\frac{5}{3}\,\,\,\,\,\,\cot⁡\theta=\frac{3}{4}\)

 

\(\textbf{5)}\) Find all 6 trig functions if the terminal side contains the point \((-5,-12)\)

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\(\sin⁡\theta=-\frac{12}{13}\,\,\,\,\,\,\cos⁡\theta=-\frac{5}{13}\,\,\,\,\,\,\tan⁡\theta=\frac{12}{5}\)
\(\csc⁡\theta=-\frac{13}{12}\,\,\,\,\,\,\sec⁡\theta=-\frac{13}{5}\,\,\,\,\,\,\cot⁡\theta=\frac{5}{12}\)

 

\(\textbf{6)}\) Find all 6 trig functions if \(\sin⁡(\theta)=-\frac{4}{5}\), Quadrant III

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\(\sin⁡\theta=-\frac{4}{5}\,\,\,\,\,\,\cos⁡\theta=-\frac{3}{5}\,\,\,\,\,\,\tan⁡\theta=\frac{4}{3}\)
\(\csc⁡\theta=-\frac{5}{4}\,\,\,\,\,\,\sec⁡\theta=-\frac{5}{3}\,\,\,\,\,\,\cot⁡\theta=\frac{3}{4}\)

 

See Related Pages\(\)

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\(\bullet\text{ Angle of Depression and Elevation}\)
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\(\bullet\text{ Convert to Radians and to Degrees}\)
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\(\bullet\text{ Area of SAS Triangles}\)
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\(\bullet\text{ Law of Cosines}\)
\(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{A}\) \(…\)

\(\bullet\text{ Area of SSS Triangles (Heron’s formula)}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\) \(…\)

\(\bullet\text{ Geometric Mean}\)
\(\,\,\,\,\,\,\,\,x=\sqrt{ab} \text{ or } \displaystyle\frac{a}{x}=\frac{x}{b}…\)

\(\bullet\text{ Geometric Mean- Similar Right Triangles}\)
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\(\bullet\text{ Inverse Trigonmetric Functions}\)
\(\,\,\,\,\,\,\,\,\sin {\left(cos^{-1}\left(\frac{3}{5}\right)\right)}…\)

\(\bullet\text{ Sum and Difference of Angles Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(A+B)}=\sin{A}\cos{B}+\cos{A}\sin{B}…\)

\(\bullet\text{ Double-Angle and Half-Angle Formulas}\)
\(\,\,\,\,\,\,\,\,\sin{(2A)}=2\sin{(A)}\cos{(A)}…\)

\(\bullet\text{ Trigonometry-Pythagorean Identities}\)
\(\,\,\,\,\,\,\,\,\sin^2{(x)}+\cos^2{(x)}=1…\)

\(\bullet\text{ Product-Sum Identities}\)
\(\,\,\,\,\,\,\,\,\cos{\alpha}\cos{\beta}=\left(\displaystyle\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\right)…\)

\(\bullet\text{ Cofunction Identities}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\cos{(\frac{\pi}{2}-x)}…\)

\(\bullet\text{ Proving Trigonometric Identities}\)
\(\,\,\,\,\,\,\,\,\sec{x}-\cos{x}=\displaystyle\frac{\tan^2{x}}{\sec{x}}…\)

\(\bullet\text{ Graphing Trig Functions- sin and cos}\)
\(\,\,\,\,\,\,\,\,f(x)=A \sin{B(x-c)}+D \) \(…\)

\(\bullet\text{ Solving Trigonometric Equations}\)
\(\,\,\,\,\,\,\,\,2\cos{(x)}=\sqrt{3}…\)