# Trigonometric formulas:

When you begin solving trigonometry it seems vast one, but it is not what you believe. This chapter is so much easy to solve. In this section, trigonometric formulas for class 10, 11, 12 is available. These formula include all trigonometric ratios, trigonometric identities, trigonometric sign rule, quadrant rule and some of the value of the trigonometric function of specific degrees.

## Trigonometric formulas list:

Trigonometric identities are of great use in solving question which covers the major portion of mathematics in class 10, 11 and 12th. The complete list of trigonometric formula will help you whenever and wherever you want.

## Trigonometric Ratios:

 Functions Value sin A $$\frac{P}{H}$$ cos A $$\frac{B}{H}$$ tan A $$\frac{P}{B}$$ cosec A $$\frac{H}{P}$$ sec A $$\frac{H}{B}$$ cot A $$\frac{B}{P}$$

## Trigonometric formulas based on relations:

 Functions Relations tan A $$\frac{sin\:A}{cos\:A}$$ cot A $$\frac{cos\:A}{sin\:A}$$ sec A $$\frac{1}{cos\:A}$$ cosec A $$\frac{1}{sin\:A}$$

## Negative sign convention of Trigonometric function:

The negative sign (-A) has usual meaning in terms of (2π – A).

 S.no. Function 1. sin(-A) = – sin A 2. cos(-A) = cos A 3. tan(-A) = – tan A 4. cosec(-A) = – cosec A 5. sec(-A) = sec A 6. cot(-A) = – cot A

## Sign convention in Trigonometry:

Also, common used function in quadrants:

The sign convention in these quadrant is remembered as

All School To College

i.e.

• All positive for 1st quadrant,
• Sin and cosec positive for 2nd quadrant,
• Tan and cot positive for 3rd quadrant,
• Cos and sec positive in 4th .
 S.no. Value 1. sin(90⁰-A) = cos A 2. cos(90⁰-A) = sin A 3. tan(90⁰-A) = cot A 4. cosec(90⁰-A) = sec A 5. sec(90⁰-A) = cosec A 6. cot(90⁰-A) = tan A

Revise these trigonometric formulas daily to score better in your board exams as well as for JEE, SSC etc. like competitive examination.

## Trigonometric Identities:

 S.no. Identities 1. sin2 A + cos2 A = 1 2. sec2 A – tan2 A = 1 3. cosec2 A – cot2 A = 1

## Trigonometric Formula As Product Rule:

 S.no. Rules 1. sin (A + B) = sin A cos B + cos A sin B 2. sin (A – B) = sin A cos B – cos A sin B 3. cos (A + B) = cos A cos B – sin A sin B 4. cos (A – B) = cos A cos B + sin A sin B 5. tan (A + B) = $$\frac{tanA + tanB}{1 – tanA\: tanB}$$ 6. tan (A – B) = $$\frac{tanA – tanB}{1 + tanA\: tanB}$$

## Trigonometric Formulas for Double Angle:

 S.no. Formulae 1. sin 2A = 2 sin A∙cos A 2. cos 2A = cos2A – sin2A=2cos2A – 1= 1 – 2sin2A 3. tan 2A = $$\frac{2tanA}{1- {tan}^{2}A}$$

## Trigonometric Formulas for Triple Angle:

 S.no. Formulae 1. Sin 3A = 3sinA – 4sin3A 2. Cos 3A = 4cos3A – 3cosA 3. Tan3A = $$\frac{3tanA – {tan}^{3}A}{1- 3{tan}^{2}A}$$ 4. Cot3A = $$\frac{{cot}^{3}A – 3cotA}{3{cot}^{2}A – 1}$$

## Trigonometric product conversion:

 S.no. Formulae 1. $$\frac{cos(A – B) – cos(A+B)}{2}$$ = sinA.sinB 2. $$\frac{cos(A – B) + cos(A+B)}{2}$$ = cosA.cosB 3. $$\frac{sin(A + B) + sin(A – B)}{2}$$ = sinA.cosB 4. $$\frac{cos(A + B) + sin(A – B)}{2}$$ = cosA.sinB

## Extended product rule:

 S.no. Formulae 1. sinA.sinB = $$\frac{cos\frac{(A + B)}{2}.cos\frac{(A-B)}{2}}{2}$$ 2. cosA.cosB = $$\frac{cos\frac{(A + B)}{2}.sin\frac{(A-B)}{2}}{2}$$ 3. sinA.cosB = $$\frac{sin\frac{(A + B)}{2}.cos\frac{(A-B)}{2}}{2}$$ 4. cosA.sinB = $$\frac{sin\frac{(A + B)}{2}.sin\frac{(A-B)}{2}}{2}$$

## Trigonometric Half Angle Identities:

 S.no. Formulae 1. $$\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}$$ 2. $$\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}$$ 3. $$\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}$$ 4. $$\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}$$ Also, $$\tan(\frac{x}{2}) =\frac{1-\cos(x)}{\sin(x)}$$

Trigonometric formulas will make you easy to solve questions. Keep a bookmark of this site to learn and revise it regularly. Class 10th trigonometric formula is here with complete evaluation.

## Trigonometric ratio of some specific angles:

The trigonometric ratio of 0°, 30°, 45°, 60°, 90° is mentioned below. take a look at it.

 ∠A 0⁰ 30⁰ 45⁰ 60⁰ 90⁰ sin A 0 $$\frac{1}{2}$$ $$\frac{1}{\sqrt{2}}$$ $$\frac{\sqrt{3}}{2}$$ 1 cos A 1 $$\frac{\sqrt{3}}{2}$$ $$\frac{1}{\sqrt{2}}$$ $$\frac{1}{2}$$ 0 tan A 0 $$\frac{1}{\sqrt{3}}$$ 1 $$\sqrt{3}$$ Not defined sec A 1 $$\frac{2}{\sqrt{3}}$$ $$\sqrt{2}$$ 2 Not defined cot A Not defined $$\sqrt{3}$$ 1 $$\frac{1}{\sqrt{3}}$$ 0 cosec A Not defined 2 $$\sqrt{2}$$ $$\frac{2}{\sqrt{3}}$$ 1