# 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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