Question

share trigonometry table and describe it​

Answer 1

Trigonometry is the branch of mathematics which deals with the relationship between the sides of a triangle (Right-angled triangle) and its angles.

All the trigonometric functions are related to the sides of the triangle and their values can be easily found by using the following relations:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

Cot = 1/Tan = Adjacent/Opposite

Cosec = 1/Sin = Hypotenuse/Opposite

Sec = 1/Cos = Hypotenuse/Adjacent

By using a right-angled triangle as a reference, the trigonometric functions or identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.

Trigonometry is a branch of Mathematics, which deals with establishing relationships between lengths of sides and angles of a triangle. It has wide applications in the field of oceanography primarily. Moreover, there are other applications in real-life areas such as music and other sound waves.

$\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} }, & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

About trigonometry: Trigonometry is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees. The commonly used trigonometry angles are 0°, 30°, 45°, 60°, and 90°.

Why a Trig Table?

The values of trigonometric ratios of standard angles are essential to solve trigonometry problems. Therefore, it is necessary to remember the values of the trigonometric ratios of these standard angles.

The trigonometric table is useful in the number of areas. It is essential for navigation, science, and engineering. This table was effectively used in the pre-digital era, even before the existence of pocket calculators. Further, the table led to the development of the first mechanical computing devices. Another important application of trigonometric tables is the Fast Fourier Transform (FFT) algorithms.

Very important basic trigonometry values

$\begin{tabular}{| c | c | c | c | c | c |}\cline{ 1-6 }\multicolumn{6}{| c |}{Trigonometric Values} \\\cline{ 1-6}Angle&0^{\circ}&30^{\circ}&45^{\circ}&60^{\circ}&90^{\circ}\\\cline{ 1-6 } sin\theta & 0 & 1/2 & 1/\sqrt{2} & 3/\sqrt{2} & 1\\cos\theta & 1 & \sqrt{3}/2 & 1 & 1/2 & 0\\tan\theta & 0 & 1/\sqrt{3} & 1 & \sqrt{3} & nd\\cot\theta& nd & \sqrt{3} & 1 & 1/\sqrt{3} & 0\\sec\theta & 1 & 2/\sqrt{3} & \sqrt{2} & 2 & nd\\cosec\theta & nd & 2 & \sqrt{2} & 2/\sqrt{3} & 1\\\cline{1-6} \end{tabular}$

 

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