1. \(\sin 30˚ = \frac{1}{2}\) ; \(\sin 30˚ = \frac{\frac{1}{\sqrt 3}}{\frac{2}{\sqrt 3}}\) ;
\(\sin 30˚ = \frac{1}{2}\)
Note that the ratios are the same: \(\frac{1}{2}\)
\(\cos 30˚ = \frac{\sqrt 3}{2}\); \(\cos 30˚ = \frac{1}{\frac{2}{\sqrt 3}}\);
\(\cos 30˚ = \frac{\frac{\sqrt 3}{2}}{1}\) ; \(\cos 30˚ = \frac{ \frac{\sqrt 3}{2}}{1}\).
Note that the ratios are the same: \(\frac{\sqrt 3}{2}\)
2. \(\sin 60˚ = \frac{\sqrt 3}{2}\) ;\(\sin 60˚= \frac{1}{\frac{2}{\sqrt 3}}\); \(\sin 60˚ = \frac{\sqrt 3}{2}\). Note: The ratios are all \(\frac{\sqrt 3}{2}\).
\(\cos 60˚ = \frac{1}{2}\); \(\cos 60˚ = \frac{\frac{1}{\sqrt 3}}{\frac{2}{\sqrt 3}}\);
\(\cos 60˚ = \frac{1}{2}\).
Note that the ratios are the same: \(\frac{1}{2}\)
3. \(\sin 45˚ = \frac{1}{\sqrt 2}\); \(\cos 45˚ = \frac{1}{\sqrt 2}\) or \(\frac{\sqrt 2}{2}\)
\(\sin 45˚ =\frac{1}{\sqrt 2}\); \(\cos 45˚=\frac{1}{\sqrt 2}\) or \(\frac{\sqrt 2}{2}\)
4. The legs of the right triangle are the same length.
5.
| Angle | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| Θ | ||||||
| 30° | \(\frac{1}{2}\) | \(\frac{√3}{2}\) | \(\frac{√3}{3}\) | 2 | \(\frac{2}{√3}\) | \(√3\) |
| 60° | \(\frac{√3}{2}\) | \(\frac{1}{2}\) | \(√3\) | \(\frac{2√3}{3}\) | 2 | \(\frac{√3}{3}\) |
| 45° | \(\frac{√2}{2}\) | \(\frac{√2}{2}\) | 1 | \(√2\) | \(√2\) | 1 |
6. Note that \(\sin 30˚ = \cos 60˚\); \(\sin 60˚ = \cos 30˚\); \(\tan 30˚ = \tan 60˚\);
\(\sin 45˚ = \cos45˚\) ;
Reciprocals: \(\csc Θ = \frac{1}{\sin Θ}\); \(\sec Θ =\frac{1}{\cos Θ}\);
\(\cot Θ = \frac{1}{\tan Θ}\)
7. You probably learned SOHCAHTOA in high school.