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Answer:
Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus. Here, we will study the relationship between the sides and angles of a right-angled triangle. The basics of trigonometry define three primary functions which are sine, cosine and tangent.
Table of contents:
Trigonometric Ratios (Sin, Cos, Tan)
Six Trigonometric Functions
Trigonometric Angles
Table
Unit Circle
Formulas
Identities
Euler’s Formula
Basics of Trigonometry
Examples
Applications
Solved Problems
FAQs
Step-by-step explanation:
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Step-by-step explanation:
Trigonometric Ratios
Trigonometric RatiosOpposite & Adjacent Sides in a Right Angled Triangle
Trigonometric RatiosOpposite & Adjacent Sides in a Right Angled TriangleIn 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.
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Trigonometric Ratios
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/AC
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/ACcos A=adjacent side/hypotenuse=AB/AC
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/ACcos A=adjacent side/hypotenuse=AB/ACtan A=opposite side/adjacent side=BC/AB
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/ACcos A=adjacent side/hypotenuse=AB/ACtan A=opposite side/adjacent side=BC/ABcosec A=hypotenuse/opposite side=AC/BC
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/ACcos A=adjacent side/hypotenuse=AB/ACtan A=opposite side/adjacent side=BC/ABcosec A=hypotenuse/opposite side=AC/BCsec A=hypotenuse/adjacent side=AC/AB
Trigonometric RatiosFor the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:sin A=opposite side/hypotenuse=BC/ACcos A=adjacent side/hypotenuse=AB/ACtan A=opposite side/adjacent side=BC/ABcosec A=hypotenuse/opposite side=AC/BCsec A=hypotenuse/adjacent side=AC/ABcot A=adjacent side/opposite side=AB/BC
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Visualization of Trigonometric Ratios Using a Unit Circle
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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.
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQ
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQtanθ=PQ/OQ=sinθ/cosθ
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQtanθ=PQ/OQ=sinθ/cosθcosecθ=OP/PQ=1/PQ
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQtanθ=PQ/OQ=sinθ/cosθcosecθ=OP/PQ=1/PQsecθ=OP/OQ=1/OQ
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQtanθ=PQ/OQ=sinθ/cosθcosecθ=OP/PQ=1/PQsecθ=OP/OQ=1/OQcotθ=OQ/PQ=cosθ/sinθ
Visualization of Trigonometric Ratios Using a Unit CircleDraw 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=PQcosθ=OQ/OP=OQ/1=OQtanθ=PQ/OQ=sinθ/cosθcosecθ=OP/PQ=1/PQsecθ=OP/OQ=1/OQcotθ=OQ/PQ=cosθ/sinθUnit circle