Question

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

Define Trigonometry.

Only For:-
❒Moderators
❒Brainly Stars
❒Other Best Users

No spamming​

Answer 1

$\huge\purple{Trigonometry.}$

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

$\huge \blue{formulas}$

• Basic Trig Ratio Formulas: These are trigonometry formulas relating to the basic trigonometric ratios sin, cos, tan, etc.
• Reciprocal Identities: This includes trigonometry formulas dealing with the reciprocal relationship between trig ratios.
• Trigonometric Ratio Table: Trigonometry values are depicted for standard angles in the trigonometry table.
• Periodic Identities: These comprise trigonometry formulas that help in finding values of trig functions for a shift in angles by π/2, π, 2π, etc.
• Co-function Identities: Trigonometry formulas for cofunction identities depict interrelationships between the trigonometry functions.
• Sum and Difference Identities: These trigonometry formulas are used to find the value of the trigonometry function for the sum or difference in angles.
• Half, Double and Triple Identities: These trigonometry formulas include values of trig functions for half, double or triple angles.
• Sum to Product Identities: These trigonometry formulas are used to represent the product of trigonometry functions as their sum or vice-versa.
• Inverse Trigonometry Formulas: Inverse trigonometry formulas include the formulas related to inverse trig functions like sine inverse, cosine inverse, etc.
• Sine Law and Cosine Law

Trigonometric Ratios

There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.

cot θ = 1/tan θ = Base/Perpendicualr

sec θ = 1/cos θ = Hypotenuse/Base

cosec θ = 1/sin θ = Hypotenuse/Perpendicular

$\huge \: \red{example}$

Example 1: The building is at a distance of 150 feet from point A. Can you calculate the height of this building if tan θ = 4/3 using trigonometry?

The base and height of the building form a right-angle triangle. Now apply the trigonometric ratio of tanθ to calculate the height of the building.

In Δ ABC, AC = 150 ft, tanθ = (Opposite/Adjacent) = BC/AC

4/3 = (Height/150 ft)

Height = (4×150/3) ft = 200ft

Answer: The height of the building is 200ft.