- What is the value of sin?
- Who invented sine?
- How is the law of sines used in real life?
- Why Sine is called sine?
- How do you go from sin to cos?
- What are the 3 trigonometric functions?
- What’s the difference between a sin and cos graph?
- What does a sine curve look like?
- How is sine derived?
- What is sine used for?
- What is sin used to find?
- Why is it called trigonometry?
What is the value of sin?
The function f(x) = sin x has all real numbers in its domain, but its range is −1 ≤ sin x ≤ 1.
The values of the sine function are different, depending on whether the angle is in degrees or radians.
The function is periodic with periodicity 360 degrees or 2π radians..
Who invented sine?
Hipparchus of NicaeaThe first trigonometric table was apparently compiled by Hipparchus of Nicaea (180 – 125 BCE), who is now consequently known as “the father of trigonometry.” Hipparchus was the first to tabulate the corresponding values of arc and chord for a series of angles.
How is the law of sines used in real life?
You can use the Law of Sines to solve real-life problems involving oblique triangles. For instance, in Exercise 44 on page 438, you can use the Law of Sines to determine the length of the shadow of the Leaning Tower of Pisa.
Why Sine is called sine?
In mathematics, the sine is a trigonometric function of an angle. … The word “sine” (Latin “sinus”) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.
How do you go from sin to cos?
The Basic Two: Sine and Cosine(1) Memorize: sine = (opposite side) / hypotenuse. … (2) sin A = cos(90° − A) or cos(π/2 − A) cos A = sin(90° − A) or sin(π/2 − A)(3) Memorize: … (4) tangent = (opposite side) / (adjacent side)(5) Memorize: … (6) tan A = cot(90° − A) or cot(π/2 − A) … (7) sec A = csc(90° − A) or csc(π/2 − A)
What are the 3 trigonometric functions?
The most widely used trigonometric functions are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used in modern mathematics.
What’s the difference between a sin and cos graph?
In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.
What does a sine curve look like?
The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1]. See how we find the graph of y=sin(x) using the unit-circle definition of sin(x).
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”).
What is sine used for?
The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. Example: Imagine a ship that is tethered to an anchor on the ocean floor.
What is sin used to find?
Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .
Why is it called trigonometry?
The word trigonometry comes from the Greek words trigonon (“triangle”) and metron (“to measure”).