Problems

\(\textbf{1)}\) \( \cos^{-1}(-1) \)

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The answer is \( θ= 180° \) or \( x=π \)

 

\(\textbf{2)}\) \( \sin^{-1} \left(-\frac{1}{2}\right) \)

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The answer is \( θ=-30° \) or \( x=-\displaystyle\frac{π}{6} \)

 

\(\textbf{3)}\) \( \tan^{-1} \left(-\sqrt{3}\right) \)

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The answer is \( θ=-60° \) or \( x=-\displaystyle\frac{π}{3} \)

 

\(\textbf{4)}\) \( \cos^{-1} \left(\frac{1}{2}\right) \)

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The answer is \( θ=60° \) or \( x=\displaystyle\frac{π}{3} \)

 

\(\textbf{5)}\) \( \sin^{-1} \left(\frac{\sqrt{3}}{2}\right) \)

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The answer is \( θ=60° \) or \( x=\displaystyle\frac{π}{3} \)

 

\(\textbf{6)}\) \( \tan^{-1} (1) \)

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The answer is \( θ=45° \) or \( x=\displaystyle\frac{π}{4} \)

 

\(\textbf{7)}\) \( \cos^{-1} (0) \)

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The answer is \( θ=90° \) or \( x=\displaystyle\frac{π}{2} \)

 

\(\textbf{8)}\) \( \sin^{-1} \left(-\frac{\sqrt{2}}{2}\right) \)

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The answer is \( θ=-45° \) or \( x=-\displaystyle\frac{π}{4} \)

 

\(\textbf{9)}\) \( \tan^{-1} (0) \)

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The answer is \( θ=0° \) or \( x=0 \)

 

\(\textbf{10)}\) \( \cos^{-1} \left(-\frac{\sqrt{3}}{2}\right) \)

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The answer is \( θ=150° \) or \( x=\displaystyle\frac{5π}{6} \)

 

\(\textbf{11)}\) \( \sin^{-1} (1) \)

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The answer is \( θ=90° \) or \( x=\displaystyle\frac{π}{2} \)

 

\(\textbf{12)}\) \( \tan^{-1} \left(-\frac{\sqrt{3}}{3}\right) \)

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The answer is \( θ=-30° \) or \( x=-\displaystyle\frac{π}{6} \)

 

\(\textbf{13)}\) \( \cos^{-1} \left(\frac{\sqrt{2}}{2}\right) \)

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The answer is \( θ=45° \) or \( x=\displaystyle\frac{π}{4} \)

 

\(\textbf{14)}\) \( \sin^{-1} \left(-\frac{\sqrt{3}}{2}\right) \)

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The answer is \( θ=-60° \) or \( x=-\displaystyle\frac{π}{3} \)

 

\(\textbf{15)}\) \( \tan^{-1} (\sqrt{3}) \)

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The answer is \( θ=60° \) or \( x=\displaystyle\frac{π}{3} \)

 

\(\textbf{16)}\) \( \cos^{-1} (\sin{\left(-\frac{π}{2}\right)}) \)

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The answer is \( θ=180° \) or \( x=π \)

 

\(\textbf{17)}\) \( \cos^{-1} (\sin{⁡π}) \)

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The answer is \( θ=90° \) or \( x=\displaystyle\frac{π}{2} \)

 

\(\textbf{18)}\) \( \sin⁡\left(\cos^{-1} \left(\frac{3}{5}\right)\right) \)

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The answer is \( \displaystyle\frac{4}{5} \)

 

\(\textbf{19)}\) \(\tan\left(\sin^{-1}\left(\frac{3}{5}\right)\right)= \)

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The answer is \( \displaystyle\frac{3}{4} \)

 

 

See Related Pages\(\)

\(\bullet\text{ Right Triangle Trigonometry}\)
\(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\)

\(\bullet\text{ Angle of Depression and Elevation}\)
\(\,\,\,\,\,\,\,\,\text{Angle of Depression}=\text{Angle of Elevation}…\)

\(\bullet\text{ Convert to Radians and to Degrees}\)
\(\,\,\,\,\,\,\,\,\text{Radians} \rightarrow \text{Degrees}, \times \displaystyle \frac{180^{\circ}}{\pi}…\)

\(\bullet\text{ Degrees, Minutes and Seconds}\)
\(\,\,\,\,\,\,\,\,48^{\circ}34’21”…\)

\(\bullet\text{ Coterminal Angles}\)
\(\,\,\,\,\,\,\,\,\pm 360^{\circ} \text { or } \pm 2\pi n…\)

\(\bullet\text{ Reference Angles}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Find All 6 Trig Functions}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Unit Circle}\)
\(\,\,\,\,\,\,\,\,\sin{(60^{\circ})}=\displaystyle\frac{\sqrt{3}}{2}…\)

\(\bullet\text{ Law of Sines}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}\) \(…\)

\(\bullet\text{ Area of SAS Triangles}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\frac{1}{2}ab \sin{C}\) \(…\)

\(\bullet\text{ Law of Cosines}\)
\(\,\,\,\,\,\,\,\,a^2=b^2+c^2-2bc \cos{A}\) \(…\)

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

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

\(\bullet\text{ Geometric Mean- Similar Right Triangles}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

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

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

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

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

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

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

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

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

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