Radians.
The radian measure of an angle is given by
[latex]({fraction ~~of ~~one ~~revolution}\times 2\pi)[/latex]
Chapter 6: Radians
The radian measure of an angle is given by
[latex]({fraction ~~of ~~one ~~revolution}\times 2\pi)[/latex]
| Degrees | [latex]\dfrac{{Radians:}}{{Exact ~~Values}}[/latex] | [latex]\dfrac{{Radians: Decimal}}{{Approximations}}[/latex] |
| [latex]0°[/latex] | [latex]0[/latex] | [latex]0[/latex] |
| [latex]90°[/latex] | [latex]\dfrac{\pi}{2}[/latex] | [latex]1.57[/latex] |
| [latex]180°[/latex] | [latex]\pi[/latex] | [latex]3.14[/latex] |
| [latex]270°[/latex] | [latex]\dfrac{3\pi}{2}[/latex] | [latex]4.71[/latex] |
| [latex]360°[/latex] | [latex]2\pi[/latex] | [latex]6.28[/latex] |
[latex]\dfrac{180°}{\pi~{radians}} = 1[/latex]
To convert from radians to degrees we multiply the radian measure by [latex]\dfrac{180°}{\pi}{.}[/latex]
To convert from degrees to radians we multiply the degree measure by [latex]\dfrac{\pi}{180}{.}[/latex]
On a circle of radius [latex]r{,}[/latex] the length [latex]s[/latex] of an arc spanned by an angle [latex]\theta[/latex] in radians is
[latex]s = r\theta[/latex]
| Degrees | Radians | Sine | Cosine | Tangent |
| [latex]0°[/latex] | [latex]0[/latex] | [latex]0[/latex] | [latex]1[/latex] | [latex]0[/latex] |
| [latex]30°[/latex] | [latex]\dfrac{\pi}{6}[/latex] | [latex]\dfrac{1}{2}[/latex] | [latex]\dfrac{\sqrt{3}}{2}[/latex] | [latex]\dfrac{1}{\sqrt{3}}[/latex] |
| [latex]45°[/latex] | [latex]\dfrac{\pi}{4}[/latex] | [latex]\dfrac{1}{\sqrt{2}}[/latex] | [latex]\dfrac{1}{\sqrt{2}}[/latex] | [latex]1[/latex] |
| [latex]60°[/latex] | [latex]\dfrac{\pi}{3}[/latex] | [latex]\dfrac{\sqrt{3}}{2}[/latex] | [latex]\dfrac{1}{2}[/latex] | [latex]\sqrt{3}[/latex] |
| [latex]90°[/latex] | [latex]\dfrac{\pi}{2}[/latex] | [latex]1[/latex] | [latex]0[/latex] | undefined |
The coordinates of the point [latex]P[/latex] determined by an arc of length [latex]t[/latex] in standard position on a unit circle are
[latex](x, y) = (\cos t, \sin t)[/latex]
Let [latex]P[/latex] be the terminal point of an arc of length [latex]t[/latex] in standard position on a unit circle. The circular functions of [latex]t[/latex] are defined by
[latex][latex] \begin{aligned}[t] \cos t = x\\ \sin t = y\\ \tan t = \dfrac{y}{x},~~x \not= 0\\ \end{aligned}[/latex]
Domain: all real numbers
Range: [latex][-1,1][/latex]
Period: [latex]2\pi[/latex]
Domain: all real numbers
Range: [latex][-1,1][/latex]
Period: [latex]2\pi[/latex]
Domain: all real numbers except all the integer multiple of [latex]\dfrac{\pi}{2}[/latex]
Range: all real numbers
Period: [latex]\pi[/latex]