Trigonometry Revision Summary
1. Acute angles (less than 90°)
Trig ratios |
Reciprocal Ratios |
| `sin θ` ` = text(opposite)/text(hypotenuse)` `=a/c` |
`csc θ` ` = 1/(sin theta)` ` =text(hypotenuse)/text(opposite)` `=c/a` |
| `cos θ ` ` = text(adjacent)/text(hypotenuse)` ` =b/c` |
`sec θ ` ` = 1/(cos theta)` ` =text(hypotenuse)/text(adjacent)` ` =c/b` |
| `tan θ ` ` = text(opposite)/text(adjacent)` ` =a/b` |
`cot θ ` ` = 1/(tan theta)` ` =text(adjacent)/text(opposite)` ` =b/a` |
2. Find height of a right triangle
`sin 15.7^"o" = h/2.500`
`h=2.500\ sin 15.7^"o"`
`= 0.6765\ "km"`
3. Exact values of 45° trigonometric ratios
`sin 45^text(o)=1/sqrt2` `cosec 45^text(o)=sqrt2` `cos 45^text(o)=1/sqrt2` `sec 45^text(o)=sqrt2` `tan 45^text(o)=1` `cot 45^text(o)=1`
4. Exact values of 30-60° trigonometric ratios
`sin 30^text(o)=1/2`
`csc 30^text(o)=2`
`cos 30^text(o)=sqrt3/2`
`sec 30^text(o)=2/sqrt3`
`tan 30^text(o)=1/sqrt3`
`cot 30^text(o)=sqrt3`
`sin 60^text(o)=sqrt3/2`
`csc 60^text(o)=2/sqrt3`
`cos 60^text(o)=1/2`
`sec 60^text(o)=2`
`tan 60^text(o)` `=sqrt3/1` ` =sqrt3`
`cot 60^text(o)=1/sqrt3`
