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# 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