Introduction To Trigonometry Class 10 Notes

CBSE Class 10 Maths Trigonometry Notes:-Download PDF Here

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 $\Delta ABC$ right-angled at B, BC is the side opposite to $\angle A,$ AC is the hypotenuse and AB is the side adjacent to $\angle A.$

Trigonometric Ratios

For the right $\Delta ABC$, right-angled at $\angle B$, the trigonometric ratios of the $\angle A$ 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

To know more about Trigonometric Ratios, visit here.

Visualization of Trigonometric Ratios Using a Unit Circle

Draw a circle of the 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 $\theta$ 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

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Visualisation of Trigonometric Ratios Using a Unit Circle

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 $0^{\circ }\le \theta \le {90}^{\circ },$

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

$tan\theta$ and $sec\theta$ are not defined at  ${90}^{\circ }.$
$cot\theta$ and $cosec\theta$ are not defined at $0^{\circ }.$

Variation of trigonometric ratios from 0 to 90 degrees

As $\theta$ increases from $0^{\circ }$ to ${90}^{\circ }$

• $sin\theta$ increases from $0$ to $1$
• $cos\theta$ decreases from $1$ to $0$
• $tan\theta$ increases from $0$ to $\infty$
• $cosec\theta$ decreases from $\infty$ to $1$
• $sec\theta$ increases from $1$ to $\infty$
• $cot\theta$ decreases from $\infty$ 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

To know more about Trigonometric Ratios of Standard Angles, visit here.

Trigonometric Ratios of Complementary Angles

Complementary Trigonometric ratios

If $\theta$ is an acute angle, its complementary angle is 90${}^{}-\theta .$ The following relations hold true for trigonometric ratios of complementary angles.

• $sin({90}^{\circ }-\theta )=cos\theta$
• $cos({90}^{\circ }-\theta )=sin\theta$
• $tan({90}^{\circ }-\theta )=cot\theta$
• $cot({90}^{\circ }-\theta )=tan\theta$
• $cosec({90}^{\circ }-\theta )=sec\theta$
• $sec({90}^{\circ }-\theta )=cosec\theta$

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To know more about Trigonometric Ratios of Complementary Angles, visit here.

Trigonometric Identities

• $si{n}^2\theta +co{s}^2\theta =1$
• $1+co{t}^2\theta =coes{c}^2\theta$
• $1+ta{n}^2\theta =se{c}^2\theta$

To know more about Trigonometric Identities, visit here.