# 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 given here.

## Trigonometric Ratios

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

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

### Trigonometric Ratios

For the right Î”ABC, right-angled at âˆ B, the trigonometric ratios of the âˆ A are as follows:

• sin A=oppositeÂ side/hypotenuse=BC/AC
• cosec A=hypotenuse/oppositeÂ side=AC/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 Î¸ with the x-axis. Draw a perpendicular from P to the x-axis to cut it at Q.

• sinÎ¸=PQ/OP=PQ/1=PQ
• cosÎ¸=OQ/OP=OQ/1=OQ
• tanÎ¸=PQ/OQ=sinÎ¸/cosÎ¸
• cosecÎ¸=OP/PQ=1/PQ
• secÎ¸=OP/OQ=1/OQ
• cotÎ¸=OQ/PQ=cosÎ¸/sinÎ¸

### Relation between Trigonometric Ratios

• cosec Î¸ =1/sin Î¸
• sec Î¸ = 1/cos Î¸
• tan Î¸ = sin Î¸/cos Î¸
• cot Î¸ = cos Î¸/sin Î¸=1/tan Î¸

## Trigonometric Ratios of Specific Angles

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

For 0âˆ˜â‰¤Î¸â‰¤90âˆ˜,

• 0â‰¤sinÎ¸â‰¤1
• 0â‰¤cosÎ¸â‰¤1
• 0â‰¤tanÎ¸<âˆž
• 1â‰¤secÎ¸<âˆž
• 0â‰¤cotÎ¸<âˆž
• 1â‰¤cosecÎ¸<âˆž

tanÎ¸ and secÎ¸ are not defined atÂ  90âˆ˜.
cotÎ¸ and cosecÎ¸ are not defined at 0âˆ˜.

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

As Î¸ increases from 0âˆ˜ to 90âˆ˜

• sinÂ Î¸ increases from 0 to 1
• cosÂ Î¸ decreases from 1 to 0
• tanÂ Î¸ increases from 0 to âˆž
• cosecÂ Î¸ decreases from âˆž to 1
• secÂ Î¸ increases from 1 to âˆž
• cotÂ Î¸ decreases from âˆž to 0

### Standard values of Trigonometric ratios

 âˆ A 0o 30o 45o 60o 90o sin A 0 Â 1/2 Â 1/âˆš2 Â âˆš3/2 Â 1 cos A 1 Â âˆš3/2 1/âˆš2 Â 1/2 0 tan A 0 Â 1/âˆš3 Â 1 âˆš3 Â not defined cosec A not defined Â 2 Â âˆš2 Â 2/âˆš3 Â 1 sec A 1 2/âˆš3 âˆš2 Â 2 Â not defined cot A not defined Â âˆš3 Â 1 1/âˆš3 0

## Trigonometric Ratios of Complementary Angles

### Complementary Trigonometric ratios

If Î¸ is an acute angle, its complementary angle is 90âˆ˜âˆ’Î¸. The following relations hold true for trigonometric ratios of complementary angles.

• sinÂ (90âˆ˜âˆ’Â Î¸)Â =Â cosÂ Î¸
• cosÂ (90âˆ˜âˆ’Â Î¸)Â =Â sinÂ Î¸
• tanÂ (90âˆ˜âˆ’Â Î¸)Â =Â cotÂ Î¸
• cotÂ (90âˆ˜âˆ’Â Î¸)Â =Â tanÂ Î¸
• cosecÂ (90âˆ˜âˆ’Â Î¸)Â =Â secÂ Î¸
• secÂ (90âˆ˜âˆ’Â Î¸)Â =Â cosecÂ Î¸

## Trigonometric Identities

• sin2Î¸+cos2Î¸=1
• 1+cot2Î¸=coesc2Î¸
• 1+tan2Î¸=sec2Î¸

1. Shashank V M

NCERT

1. lavanya
2. Shalini kumari

Very nice notes .It’s really help me

3. Yugansh

Can u answer my questions of this chapter!?

1. Pramit Ranjan

What’s the question

4. found these points becoming most helpful to solve my confusion