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.
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.
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.
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
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∘
- sin θ increases from 0 to 1
- cos θ decreases from 1 to 0
- tan θ increases from 0 to ∞
- cosec θ decreases from ∞ to 1
- sec θ increases from 1 to ∞
- cot θ decreases from ∞ to 0
Standard values of Trigonometric ratios
|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 90∘−θ. The following relations hold true for trigonometric ratios of complementary angles.
- sin (90∘− θ) = cos θ
- cos (90∘− θ) = sin θ
- tan (90∘− θ) = cot θ
- cot (90∘− θ) = tan θ
- cosec (90∘− θ) = sec θ
- sec (90∘− θ) = cosec θ