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IMPORTANT DEFINITIONS AND FORMULAE

An angle is positive if its rotation is in the anticlockwise and negative if its rotation is in the clockwise direction.

If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ration of the angle can be determined.

Two angles are said to be complementary, if their sum is 900 and each one of them is called the complement of the other.

An equation with trigonometric ratios of an angle θ, which is true for all values of ‘ θ ‘, for which the given trigonometric ratios are defined, is called an identity.

The three fundamental trigonometric identities are

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$$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$$

$\vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} – \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} – \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} – \frac{\partial F_x}{\partial y} \right) \mathbf{k}$

$\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}$

$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$

$\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot nd$

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\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

x = {-b \pm \sqrt{b^2-4ac} \over 2a}[\latex]

$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

x = {-b \pm \sqrt{b^2-4ac} \over 2a}[\latex]

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$${x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

$${sqrt[n]{1+x+x^2+ldots}}$$

{sqrt[n]{1+x+x^2+ldots}}[\latex]

$${sqrt[n]{1+x+x^2+ldots}}$$

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