Introduction: Trigonometry

Trigonometry ratios-

For the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:

sin A=opposite side/hypotenuse=BC/AC

cos A=adjacent side/hypotenuse=AB/AC

tan A=opposite side/adjacent side=BC/AB

cosec A=hypotenuse/opposite side=AC/BC

sec A=hypotenuse/adjacent side=AC/AB

cot A=adjacent side/opposite side=AB/BC

Relation between the trigonometry ratios-

cosec θ =1/sin θ
sec θ = 1/cos θ
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ=1/tan θ

standard trigonometry ratios-

Complimentary trigonometry ratios-

If θ is an acute angle, its complementary angle is 90^∘−θ. The following relations hold true for trigonometric ratios of complementary angles.
sin (90^∘− θ) = cos θ
cos (90^∘− θ) = sin θ
tan (90^∘− θ) = cot θ
cot (90^∘− θ) = tan θ
cosec (90^∘− θ) = sec θ
sec (90^∘− θ) = cosec θ

Trigonometry identities-

sin²θ+cos²θ=1
1+cot²θ=coesc²θ
1+tan²θ=sec²θ

Some applications of trigonometry-

Line of sight is the line drawn from the eye of the observer to the point on the object viewed by the observer.

Horizontal level is the horizontal line through the eye of the observer.

The angle of elevation is relevant for objects above horizontal level.

It is the angle formed by the line of sight with the horizontal level.

The angle of depression is relevant for objects below horizontal level.
It is the angle formed by the line of sight with the horizontal level.

Calculating heights and distances-

Step 1: Draw a line diagram corresponding to the problem.

Step 2: Mark all known heights, distances and angles and denote unknown lengths by variables.

Step 3: Use the values of various trigonometric ratios of the angles to obtain the unknown lengths from the known lengths.