Trigonometry Part-1 || Chapter – 8 || Class 10th (For English Medium)
Trigonometry Part-2 || Chapter – 8 || Class 10th (For English Medium)
Trigonometry Part-1 || Chapter – 8 || Class 10th (For Hindi Medium)
Trigonometry Part-2 || Chapter – 8 || Class 10th (For Hindi Medium)
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
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 θ with the x-axis. Draw a perpendicular from P to the x-axis to cut it at Q.
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
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|
To know more about Trigonometric Ratios of Standard Angles, visit here.
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
To know more about Trigonometric Ratios of Complementary Angles, visit here.