Steps To Trigonometry Problems

By Author: Pierce Brosnan
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Introduction for steps to trigonometry problems:

The term trigonometry is derived from Greek, which is used for finding angle. This subject was mainly developed to solve problems in geometry. In recent times, the subject has been extended consider beyond the solution of triangles. The modern applications are of quite a different character. In this article, we are going to see general steps for trigonometry problems related to unit circle with few example problems in steps.

Steps for Trigonometry Problems Related to Unit Circle:

Step 1:Let q be any real number.

Step 2: Start at any point on a circle and calculate along the circumference of arc length |l| units.

Step 3: If q > 0 measure the arc in opposite of clockwise direction i.e., anticlockwise direction.

Step 4: If q < 0, measure the arc in normal clockwise directions.

This locates a single point on the circumference of the unit circle. We call the point then locates as the trigonometric point P(a). The real number a and the point P(a) forms an ordered pair, this defines a task whose field as the position of all real numbers ...
... and whose range is the set of all points on the unit circle. We write the ordered pairs of this function as (a, P(a)).

Example Problems of Trigonometry in Steps:

Example problem 1:

Prove the trigonometric function `sqrt((cot 2x sin 2x) (cos 2x))` = cos 2x.

Solution:

Step 1: Given trigonometry function

`sqrt((cot 2x sin 2x) (cos 2x))` = cos 2x.

Step 2: Consider the left hand side of the given function and simplify it

`sqrt((cot 2x sin 2x) (cos 2x))` = `sqrt(((cos 2x)/(sin 2x)) (sin 2x cos 2x))` Since cot 2x = `(cos 2x)/(sin 2x) `

= `sqrt((cos 2x) (cos 2x))`

= `sqrt(cos^2 2x)` .

= cos 2x .

= Right hand side of the given function

Step 3: Solution

Hence, `sqrt((cot 2x sin 2x) (cos 2x))` = cos 2x.

Example problem 2:

Prove the trigonometric function `sqrt(1+ cot^2 2x)` . = cosec 2x.

Solution:

Step 1: Given trigonometry function

`sqrt(1+ cot^2 2x)` . = cosec 2x.

Step 2: Consider the left hand side of the given function and simplify it

`sqrt(1+ cot^2 2x)` . = `sqrt(1 + (cos^2 2x)/(sin^2 2x))`. Since cot 2x = `(cos 2x)/(sin 2x) `.

= `sqrt(((sin^2 2x) + (cos^2 2x))/(sin^2 2x))`

= `sqrt(1/(sin^2 2x))` . Since sin2 x + cos2x =1 .

= `sqrt (cosec^2 2x)` .

= cosec 2x.

Step 3: Solution

Hence, `sqrt(1+ cot^2 2x)` . = cosec 2x.

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