# Introduction To Trigonometry Class 10 Notes

## CBSE Class 10 Maths Trigonometry Notes:-

The notes for trigonometry class 10 Maths is provided here. Get the complete concept on trigonometry which is covered in Class 10 Maths. Also, get the various trigonometric ratios for specific angles, the relationship between trigonometric functions, trigonometry tables, various identities are given below.

## Trigonometric Ratios

### Opposite & Adjacent Sides in a Right Angled Triangle

In the ΔABC right-angled at B, BC is the side opposite to A, AC is the hypotenuse and AB is the side adjacent to A.

### Trigonometric 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

### Visualization of Trigonometric Ratios Using a Unit Circle

Draw a circle of unit radius with the origin as the centre. Consider a line segment OP joining a point P on the circle to the centre which makes an angle θ with the x-axis. Draw a perpendicular from P to the x-axis to cut it at Q.

• sinθ=PQ/OP=PQ/1=PQ
• cosθ=OQ/OP=OQ/1=OQ
• tanθ=PQ/OQ=sinθ/cosθ
• cosecθ=OP/PQ=1/PQ
• secθ=OP/OQ=1/OQ
• cotθ=OQ/PQ=cosθ/sinθ

### Relation between Trigonometric 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

## Trigonometric Ratios of Specific Angles

### Range of Trigonometric Ratios from 0 to 90 degrees

For 0θ90,

• 0≤sinθ≤1
• 0≤cosθ≤1
• 0≤tanθ<∞
• 1≤secθ<∞
• 0≤cotθ<∞
• 1≤cosecθ<∞

tanθ and secθ are not defined at  90.
cotθ and cosecθ are not defined at 0.

### Variation of trigonometric ratios from 0 to 90 degrees

As θ increases from 0 to 90

• sinθ increases from 0 to 1
• cosθ decreases from 1 to 0
• tanθ increases from 0 to
• cosecθ decreases from to 1
• secθ increases from 1 to
• cotθ decreases from to 0

### Standard values of Trigonometric ratios

 ∠A 0o 30o 45o 60o 90o sin A 0 1/2 1/√2 √3/2 1 cos A 1 √3/2 1/√2 1/2 0 tan A 0 1/√3 1 √3 not defined cosec A not defined 2 √2 2/√3 1 sec A 1 2/√3 √2 2 not defined cot A not defined √3 1 1/√3 0

## Trigonometric Ratios of Complementary Angles

### Complementary Trigonometric ratios

If θ is an acute angle, its complementary angle is 90θ. The following relations hold true for trigonometric ratios of complementary angles.

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

## Trigonometric Identities

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