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.