Skip to main content
Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

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`

Problem Solver

AI Math Calculator Reviews

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of GPT large language models to parse and generate natural language. This creates math problem solver thats more accurate than ChatGPT, more flexible than a calculator, and faster answers than a human tutor. Learn More.

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.