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`
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