Skip to main content

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

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

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

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`


Search IntMath, blog and Forum

Search IntMath

Online Trigonometry Solver

This trigonometry solver can solve a wide range of math problems.

Trigonometry Lessons on DVD

Math videos by

Easy to understand trigonometry lessons on DVD. See samples before you commit.

More info: Trigonometry videos

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

See the Interactive Mathematics spam guarantee.