Question: What Is The Value Of Sine?

What is trigonometry formula?

Basic Formulas 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.

sec θ = Hypotenuse/Adjacent Side..

What is the largest possible value for sine?

The maximum value of the function is M = A + |B|. This maximum value occurs whenever sin x = 1 or cos x = 1. The minimum value of the function is m = A ‐ |B|. This minimum occurs whenever sin x = −1 or cos x = −1.

How is sine derived?

The concept of Sine was progressively elaborated , and here is an explanation of the etymology of the words sine , tangent and cosine : The word sine derives from Latin sinus (“bend”, “bay”, “the hanging fold of the upper part of a toga “, “the bosom of a garment”).

Where is trigonometry used?

Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings etc. It is used naval and aviation industries. It is used in cartography (creation of maps). Also trigonometry has its applications in satellite systems.

What is the minimum value of sine?

Properties Of The Sine Graph Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.

Why Sine is called sine?

The word sine comes from the Latin sinus, bosom, because early translators mistook the Arabic word for chord and thought it was the Arabic word for bosom. The “co-” prefix in cosine and cotangent simply stands for co-angle, the complementary angle. The cosine of an angle is the sine of its complementary angle.

Who invented sine?

Abu’l WafaSine was introduced by Abu’l Wafa in 8th century, as a more convenient function, and gradually spread first in the Muslim world, and then to the West. (But apparently it was used in India centuries before him), as a more convenient function.

Why is it called trigonometry?

The term “trigonometry” was derived from Greek τρίγωνον trigōnon, “triangle” and μέτρον metron, “measure”. The modern word “sine” is derived from the Latin word sinus, which means “bay”, “bosom” or “fold” is indirectly, via Indian, Persian and Arabic transmission, derived from the Greek term khordḗ “bow-string, chord”.

Who is the father of trigonometry?

HipparchusThe first trigonometric table was apparently compiled by Hipparchus, who is consequently now known as “the father of trigonometry”.

What is the maximum and minimum value of Cosec Theta?

Maximum value of cos θ is 1 when θ = 0 ˚, 360˚. Minimum value of cos θ is –1 when θ = 180 ˚.

What is the maximum value of sin?

Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.

What is period of sine function?

The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.

What is trigonometry with example?

Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. … For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

What does a sine curve look like?

The domain of the sine function As you drag the point A around notice that after a full rotation about B, the graph shape repeats. The shape of the sine curve is the same for each full rotation of the angle and so the function is called ‘periodic’. The period of the function is 360° or 2π radians.

What is the maximum value of 1 Cos A?

The minimum value of cosx is -1 (for example when x is pi radians), and so the maximum value of 1-cosx is 1-(-1) = 1+1 =2.

What is sin equal to?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). (1) Memorize: sine = (opposite side) / hypotenuse. cosine = (adjacent side) / hypotenuse.

What is the a value in a sine function?

The value A (in front of sin or cos) affects the amplitude (height). The amplitude (half the distance between the maximum and minimum values of the function) will be |A|, since distance is always positive. Increasing or decreasing the value of A will vertically stretch or shrink the graph.