Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of a triangle. It comes from two Greek words – trigonom (triangle) and metron (measure).

TRIGONOMETRY

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of a triangle. It comes from two Greek words – trigonom (triangle) and metron (measure).

There is an enormous number of the uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance between land marks. Although it was first applied in spheres, it had a greater application to planes. Surveyors have used trigonometry for many centuries.

Within mathematics, it is used in calculus (perhaps its greatest application), linear algebra, and statistics.

Trigonometric tables were created over 2000 years ago for computation in astronomy.

A student is expected to be familiar with the definitions of trigonometric ratios for acute angles.

If one angle is 90° and one of the other angles is known, the third can be determined because the three angles of any triangle add up to 180°. The two acute angles therefore add up to 90° (complimentary angles).

Once the angles are known, the ratios of the sides are determined regardless of the overall size of the triangle. If the length of one side is known, the other two are determined. These ratios are given by the following trigonometric functions of known angle, A; where a, b, and c refer to the lengths of the sides accompanying the

figure.

Sine function (sin)

This is the ratio of the opposite side of the triangle to its hypotenuse.

Cosine function (cos)

This is the ratio of the adjacent side to the hypotenuse

Cosine function (cos)

This is the ratio of the adjacent side to the hypotenuse

Tangent function (tan)

This is the ratio of the opposite to the adjacent side.

The hypotenuse is the side opposite to the 90° angle. It is the longest side of a triangle and one of the sides adjacent to A.

The term perpendicular and base are sometimes used for opposite and adjacent sides respectively.

Many people find it easy to remember what sides of the right angle are equal to sine, cosine, or tangent by memorising the mnemonic SOH-CAH-TOA.

The reciprocals of the functions are named cosecant
(cosec), secant (sec) and cotangent (cot).

Consider the following triangle ABC

Applying the Pythagoras’ theorem to triangle ABC;

Dividing equation (i) by cos2θ

Dividing Eqn (i) by sin2θ

NOTE:

More details are in the attachment below.

 

 

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