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)

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

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.

• 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

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∘≤θ≤90∘,

• 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∘

• 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

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.

Trigonometric Identities

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