Trigonometry Revision Summary

1. Acute angles (less than 90°)

Triangle with sides a,b,c

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

Right triangle with unknown height

`sin\ 15.7^"o" = h/2.500`

`h=2.500\ sin\ 15.7^"o"`

`= 0.6765\ "km"`

3. Exact values of 45° trigonometric ratios

45-45 triangle, sides 1,1, sqrt 2

`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

30-60 triangle - exact trig 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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