# CBSE Class 10th Maths

## Ch- 8 Introduction to Trigonometry

### Trigonometry:

Trigonometry is the science of relationships between the sides and angles of a right-angled triangle.

### Trigonometric Ratios:

Ratios of sides of right triangle are called trigonometric ratios.
Consider triangle ABC right-angled at B. These ratios are always defined with respect to acute angle ‘A’ or angle ‘C.

 case I case II (i) sine A = $frac { perpendicular }{ hypotenuse } =frac { BC }{ AC }$ (i) sine C = $frac { perpendicular }{ hypotenuse } =frac { AB }{ AC }$ (ii) cosine A = $frac { base }{ hypotenuse } =frac { AB }{ AC }$ (ii) cosine C = $frac { base }{ hypotenuse } =frac { BC }{ AC }$ (iii) tangent A = $frac { perpendicular }{ base } =frac { BC }{ AB }$ (iii) tangent C = $frac { perpendicular }{ base } =frac { AB }{ BC }$ (iv) cosecant A = $frac { hypotenuse }{ perpendicular } =frac { AC }{ BC }$ (iv) cosecant C = $frac { hypotenuse }{ perpendicular } =frac { AC }{ AB }$ (v) secant A = $frac { hypotenuse }{ base } =frac { AC }{ AB }$ (v) secant C = $frac { hypotenuse }{ base } =frac { AC }{ BC }$ (v) cotangent A = $frac { base }{ perpendicular } =frac { AB }{ BC }$ (v) cotangent C = $frac { base }{ perpendicular } =frac { BC }{ AB }$

TRIGONOMETRIC IDENTITIES:

• sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ ⇒ cos² θ = 1 – sin² θ
• cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1
• sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

• si(90θcoθ
• co(90θsiθ
• ta(90θcoθ
• co(90θtaθ
• cose(90θseθ
• se(90θcoseθ