## 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-**

sin^{2}θ+cos^{2}θ=1

1+cot^{2}θ=coesc^{2}θ

1+tan^{2}θ=sec^{2}θ

**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.