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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

2.500 km h
15.70o

Triangle with unknown height h.

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

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

`= 0.6765\ "km"`

3. Exact values of 45° trigonometric ratios

1 1
`sqrt(2)`
`45^"o"`
`45^"o"`

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

2 1
`sqrt(3)`
`60^"o"`
`30^"o"`

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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