Question

Hello guys first of all how are you all in this pandemic situation ? How are online classes going on? Can anyone explain me what are trigonometry ratios? Please don't delete my question.

Answer 1

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Trigonometric Ratios

• "Trigon" is Greek for triangle , and "metric" is Greek for measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90°90° ). Remember that the two sides of a right triangle which form the right angle are called the legs , and the third side (opposite the right angle) is called the hypotenuse .
• There are three basic trigonometric ratios: sine , cosine , and tangent . Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non- 90°90° angles.
• sine=length of the leg opposite to the anglelength of hypotenuse   abbreviated "sin"cosine=length of the leg adjacent to the anglelength of hypotenuse   abbreviated "cos"tangent=length of the leg opposite to the anglelength of the leg adjacent to the angle   abbreviated "tan"sine=length of the leg opposite to the anglelength of hypotenuse   abbreviated "sin"cosine=length of the leg adjacent to the anglelength of hypotenuse   abbreviated "cos"tangent=length of the leg opposite to the anglelength of the leg adjacent to the angle   abbreviated "tan"

Example:

Write expressions for the sine, cosine, and tangent of ∠A∠A .

The length of the leg opposite ∠A∠A is aa . The length of the leg adjacent to ∠A∠A is bb , and the length of the hypotenuse is cc .

The sine of the angle is given by the ratio "opposite over hypotenuse." So,

sin∠A=acsin∠A=ac

The cosine is given by the ratio "adjacent over hypotenuse."

cos∠A=bccos∠A=bc

The tangent is given by the ratio "opposite over adjacent."

tan∠A=abtan∠A=ab

Generations of students have used the mnemonic " SOHCAHTOA " to remember which ratio is which. ( S ine: O pposite over H ypotenuse, C osine: A djacent over H ypotenuse, T angent: O pposite over A djacent.)

Other Trigonometric Ratios

The other common trigonometric ratios are:-

secant=length of hypotenuselength of the leg adjacent to the angle   abbreviated "sec" sec(x)=1cos(x)cosecant=length of hypotenuselength of the leg opposite to the angle   abbreviated "csc" csc(x)=1sin(x)secant=length of the leg adjacent to the anglelength of the leg opposite to the angle   abbreviated "cot" cot(x)=1tan(x)secant=length of hypotenuselength of the leg adjacent to the angle   abbreviated "sec" sec(x)=1cos(x)cosecant=length of hypotenuselength of the leg opposite to the angle   abbreviated "csc" csc(x)=1sin(x)secant=length of the leg adjacent to the anglelength of the leg opposite to the angle   abbreviated "cot" cot(x)=1tan(x)

Write expressions for the secant, cosecant, and cotangent of ∠A∠A .

The length of the leg opposite