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# Trigonometric ratios

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This presentation illustrates the concepts of trigonometric ratios

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### Trigonometric ratios

1. 1. Trigonometric Ratios by SBR www.harekrishnahub.com
2. 2. www.harekrishnahub.com Consider a circle with centre πΆ and radius π units. Let π· (π, π) be any point on the circumference of the circle. Join πΆπ·. Let the radius vector πΆπ· make an angle π½ with the positive π β ππππ. β΄ β πΏπΆπ· = π½ and πΆπ· = π Draw π·π΄ β the π β ππππ. β΄ πΆπ΄ = π and π·π΄ = π
3. 3. www.harekrishnahub.com π·π΄πΆ form a right angle triangle as shown below. Let us identify each of the sides of the triangle. πΆπ· = π = π π + π π is the hypotenuse π·π΄ = π, the side opposite to π½ is called the opposite side. πΆπ΄ = π, the side adjacent to π½ is called the adjacent side.
4. 4. www.harekrishnahub.com 6 trigonometric ratios Sine of angle ΞΈ π ππ π πππππ ππ‘π π πππ βπ¦πππ‘πππ’π π π π = π π π + π π CoSine of angle ΞΈ πππ  π ππππππππ‘ π πππ βπ¦πππ‘πππ’π π π π = π π π + π π Tangent of angle ΞΈ π‘ππ π πππππ ππ‘π π πππ ππππππππ‘ π πππ π π for x β  0 CoSecant of angle ΞΈ πππ ππ π βπ¦πππ‘πππ’π π πππππ ππ‘π π πππ π π = π π + π π π for y β  0 Secant of angle ΞΈ π ππ π βπ¦πππ‘πππ’π π ππππππππ‘ π πππ π π = π π + π π π for x β  0 CoTangent of angle ΞΈ πππ‘ π ππππππππ‘ π πππ πππππ ππ‘π π πππ π π for y β  0
5. 5. www.harekrishnahub.com But πππ π½ = ππππππππ ππππ ππππππππ ππππ We have, πππ π½ = ππππππππ ππππ ππππππππππ ππππππππ ππππ ππππππππππ Dividing both the numerator and the denominator by hypotenuse, we get πππ π½ = ππππππππ ππππ ππππππππππ πππ π½ = ππππππππ ππππ ππππππππππ β΄ πππ π½ = πππ π½ πππ π½
6. 6. www.harekrishnahub.com Reciprocal relations πππ π½ = πΆππ ππππ πππ = π πππ πΆππ ππππ = π πππππ π½ πππ π½ = πππ ππππ πππ = π πππ πΆππ ππππ = π πππ π½ πππ π½ = πΆππ ππππ πππ ππππ = π πππ ππππ πΆππ ππππ = π πππ π½ Therefore, πππ π½ and πππππ π½ are reciprocal to each other Therefore, πππ π½ and πππ π½ are reciprocal to each other Therefore, πππ π½ and πππ π½ are reciprocal to each other