Trigonometric Functions
Trigonometric Functions Important Notes
Conversion Formulas (i) Degree to Radian Radian measure = $\frac{\pi }{180}$ × Degree measure (ii) Radian to Degree Degree measure = $\frac{18…
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Trigonometric Functions
Trigonometric Functions Miscellaneous Exercise
Prove that 1. $2\cos \frac{\pi}{13}\cos \frac{9\pi}{13}$ $+\cos\frac{3\pi}{13}+\cos\frac{5\pi}{13}=0$ L.H.S., = $2\cos \frac{\pi}{13}\cos \frac{…
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Trigonometric Functions
Trigonometric Functions Exercise 3.4
Find the principal and general solutions of the following equations: 1. $\tan x =\sqrt{3}$ We know that, $\tan \frac{\pi}{3} =\sqrt{3}$ and $\t…
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Trigonometric Functions
Trigonometric Equations
An equation involving trigonometric functions of a variable is called a trigonometric equation. A solution of trigonometric equation is a value of…
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Trigonometric Functions
Trigonometric Functions Exercise 3.3
Prove that 1.$\sin^{2}\frac{\pi }{6}+\cos^{2}\frac{\pi }{3}-\tan^{2}\frac{\pi }{4}=-\frac{1}{2}$ L.H.S., = $\left ( \frac{1}{2} \right )^{2}+\le…
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Trigonometric Functions
Trigonometric Functions of Sum and Difference of Angles
Consider a unit circle with centre O at the origin. Let A be the point (1,0). Let P, Q and R be the points on the circle such that, arc AP = x…
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Trigonometric Functions
Trigonometric Functions Exercise 3.2
Find the values of other five trigonometric functions. 1. cos x = $\displaystyle \small -\frac{1}{2}$ , x lies in third quadrant We know that, $\…
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Trigonometric Functions
Trigonometric Functions
Trigonometric Ratios Let a rotating ray starts from initial position OA and move about O and trace out an angle ∠ AOB = x. Consider the right a…
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Trigonometric Functions
Trigonometric Functions Exercise 3.1
1. Find the radian measures corresponding to the following degree measures: (i) 25° $\displaystyle \small 25^{\circ}=\left ( \frac{\pi }{180} \ri…
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Trigonometric Functions
Degree and Radian Measure of Angle
Angle An angle is made up of two rays with a common end point. This end point is the vertex of the angle. The rays are the sides of the angle. A…
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