Math Assignment Help >> Trigonometry, Triangle Measurement

Trigonometry is branch of Mathematics that means “triangle measurement”. Trigonometry was only concerned with establishing relations between the angles of a triangle and sides of triangle, but now these days it is applied in its application in various branches of science for example engineering, navigation, surveying etc. The knowledge of trigonometry is essential for every branch of higher mathematics.

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Main Trigonometry Topics:

Angles, Radian or Quadrants

An angle is shown as the amount of rotation of a revolving line that is from the initial position to the terminal position. The counter−clockwise rotation is called positive or the clockwise is called negative. One radian, shown as is measured of an angle subtended at the centre O of circle of radius r by an arc of r length. To express the measurement of an angle as a real number, we generally use radian measure. An angle is known to be in a particular quadrant, if the terminal side of the angle in standard position lies within that quadrant.

Trigonometrically Ratios and Identities

This is study about the six trigonometric ratios. These are sine, cosine, cosecant, tangent, secant, cotangent and their applications.

a) Periodic function: A function f(x) is called to be a periodic function with period α only if f(x + α) = f(x). The least positive value of α is known the fundamental period of the function. All circular functions or trigonometrical functions are periodic functions.

Compound Angles

Section is discussed with the trigonometrical ratios of compound angles such as A + B, A − B, in terms of trigonometrical ratios of A, B. The relation f(x + y) = f(x) + f(y) is not true for all functions of a real variable, this should be noted and it is very important. This section is concerned with developing the trigonometric ratios of the compound angles and it helps in finding the value of any unknown angle in terms of know angles. Identities involving sin2A, cos2A, tan3A and others are known multiple angle identities.

Trigonometrically Equations

An equation that involves trigonometrical function is known a trigonometrical equation.

cosθ =1/2 , cos2θ − 2sinθ =1/2, tanθ = 0 are examples for trigonometrical equations. To prove these equations we get all replacements for the variable θ which make the equations true. The trigonometrical equation’s solution is the value of the unknown angle which satisfies the equation. A trigonometrical equation can have infinite number of solutions and solution in which the absolute value of the angle is the least is known principal solution.

Properties of Triangles

List of properties and formulas of triangles are discussed in this section.

Solution of Triangles

The methods of finding the unknown parts of a triangle are known the solutions of triangle. If three parts of a triangle and atleast one of which is a side are given then the other parts may be find out. Here, we shall concern the following three stages.

1) Three sides are shown in figure.

2) Any one side and two angles are shown in figure.

3) Any two sides and the included angle are shown in figure.

Inverse Trigonometrical functions (Inverse circular functions)

The quantities sin^-1x, cos^-1x, tan^-1x, … are known as inverse circular functions. sin^-1x is an angle θ, whose sine is x and cos^-1x denotes an angle whose cosine is x or so on. The principal value of an inverse function is which value of the general value that is numerically the least. It may be positive-negative. If there are two values, one positive and the other negative so that they are numerically equal, then the principal value is the positive one.