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Trigonometric Ratios Calculator
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Trigonometric ratio tells how the sides and angles are related to each other in a triangle.There are six trigonometric ratios in a triangle i.e., sin x, cos x, tan x, cosec x, sec x, cot x. Lets take a right angled triangle.There are three sides in a right angled triangle - base, perpendicular side and hypotenuse as in fig
Trigonometric ratio calculator is a online tool to calculate any trigonometric angle if the side lengths are known. You just have to enter the side lengths in space provided and get the trigonometric ratio angle value instantly.The base is the adjacent side, perpendicular is the opposite side and largest side is the hypotenuse in a triangle.

## Steps for Trigonometric Ratios Calculator

Step 1 :

Read the problem and observe whether all three side lengths are given, note it down.

Step 2 :

The trigonometric ratios are given as

sin $\theta$ = $\frac{Perpendicular\ side}{Hypotenuse}$

cos $\theta$ = $\frac{Base}{Hypotenuse}$

tan $\theta$ = $\frac{Perpendicular\ side}{Adjacent\ side}$

cosec $\theta$ = $\frac{Hypotenuse}{Perpendicular\ side}$

sec $\theta$ = $\frac{Hypotenuse}{Base\ side}$

cot $\theta$ = $\frac{Base\ side}{Perpendicular\ side}$

If the base is called the adjacent side, perpendicular the opposite side and largest side is the hypotenuse in a triangle

sin $\theta$ = $\frac{opposite}{hypotenuse}$

cos $\theta$ = $\frac{adjacent}{hypotenuse}$

tan $\theta$ = $\frac{opposite}{adjacent}$

cosec $\theta$ = $\frac{hypotenuse}{opposite}$

sec $\theta$ = $\frac{hypotenuse}{adjacent}$

cot $\theta$ = $\frac{adjacent}{opposite}$

Substitute the given side values in above formula and get the trigonometric angles.

## Problems on Trigonometric Ratios Calculator

1. ### Evaluate sin $\theta$ and sec $\theta$ if base length is 3 cm, perpendicular length is 4 cm and hypothenuse is 5 cm.

Step 1 :

Given: Base length = 3 cm, perpendicular length = 4 cm and hypothenuse = 5 cm

Step 2 :

To find sin $\theta$ and sec $\theta$
sin $\theta$ = $\frac{Perpendicular\ length}{hypotenuse}$

= $\frac{4\ cm}{5\ cm}$

= 0.8

sec $\theta$ = $\frac{Hypotenuse}{Base\ side}$

= $\frac{5\ cm}{3\ cm}$

= 1.667.

sin $\theta$ = 0.8, sec $\theta$ = 1.667.

2. ### Evaluate the value of tan $\theta$ and cot $\theta$ if base length is 4 cm and perpendicular length is 6 cm.

Step 1 :

Given: Base length = 4 cm, perpendicular length = 6 cm, hypothenuse = ?

Hypothenuse is given by

Hypothenuse = $\sqrt{(Base length)^2 + (Perpendicular length)^2}$

= $\sqrt{(4)^2 + (6)^2}$

= 7.21 cm

Step 2 :

To evaluate tan $\theta$ and cot $\theta$

tan $\theta$ = $\frac{Perpendicular\ length}{Base\ length}$

= $\frac{6\ cm}{4\ cm}$

= 1.5

cot $\theta$ = $\frac{1}{tan\ \theta}$

= $\frac{1}{1.5}$

= 0.667.

tan $\theta$ = 1.5 and cot $\theta$ = 0.667