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# Trigonometry Practice

"Trigonometry" is an important branch of mathematics.  The word Trigonometry is derived from the Greek words: 'trigonon' and 'metron'. The word 'trigonon' means a triangle and the word 'metron' means measure. Hence, trigonometry means the science of measuring triangles.

In other words, it is the branch of mathematics which deals with the measurement of the sides and the angles of a triangle and the problems allied with angles.

The basic functions of the trigonometry as follows:

$Sin A$ = $\frac{opposite }{ Hypotenuse}$

$Cos A$ = $\frac{Adjacent}{ Hypotenuse}$

$Tan A$ = $\frac{opposite }{Adjacent}$

$sec A$ = $\frac{1}{cos A}$

$cosec A$ = $\frac{1}{sin A}$

$Cot A$ = $\frac{cos A}{Sin A}$

Trigonometry identity formula:

$cos^2A + sin^2A = 1$

$1 + tan^2A = sec^2A$

$cot^2A + 1 = cosec^2A$

Triangle $ABC$ is any triangle with side lengths $a, b, c$

 Related Calculators Calculator for Trigonometry Right Angle Trigonometry Calculator Right Triangle Trigonometry Calculator Trigonometry Function Calculator

## Examples

Example 1: Consider the right triangle given that $\theta = 45^{\circ}$ and if the measure of the hypotenuse is 3,find the measure of other 2 sides.

Solution: Using the formula we can write

$sin 45^{\circ}$ = $\frac{a}{2}$......(1)

$cos 45^{\circ}$ = $\frac{b}{2}$....(2)

Find $sin 45$ amd cos 45 using calculator

$sin 45 = 0.707$ and $cos 45 = 0.707$

Substitute in equation 1 and 2 we get

0.707 = $\frac{a}{2}$ => $a = 1.414$

0.707 = $\frac{b}{2}$ => $b = 1.414$

We can see that the measures of a and b are equal.

Example 2: Prove that $\frac{cot x}{cosec x}$ = $cos x$

Solution: Consider LHS $\frac{cot x}{cosec x}$....(1)

Since $cotx$ = $\frac{cosx}{sinx}$ and $cosec x$ = $\frac{1}{sin x}$

Substitute in (1) we get

= $\frac{\frac{cos x}{sin x}}{\frac{1}{sinx}}$

= $\frac{cos x}{sin x}$ $\frac{sinx}{1}$

= $cos x$

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