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What are trig ratios?
Trig ratios or to give them their proper name are trigonometrical rations applicable to right angle triangles and they are tangent ratio, sine ratio and cosine ratio.
Why do sine and cosine always have values less than 1?
Sine and cosine functions represent the ratios of the lengths of sides of a right triangle relative to the hypotenuse. Since these ratios involve the lengths of the triangle's legs (which are always shorter than or equal to the hypotenuse), the values of sine and cosine cannot exceed 1. Additionally, on the unit circle, the coordinates of any point (x, y) are constrained within the range of -1 to 1, which further reinforces that the maximum and minimum values of sine and cosine are also limited to this range.
What are the trigonometric functions and ratios?
In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic. Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos. Tangent is the third basic ratio defined as Sin/Cos. For each of these three, there is a corresponding reciprocal function: Sine -> Cosecant (cosec or csc) Cosine -> Secant (sec) Tangent -> Cotangent (cot). Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1. The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.
Why are there two sine cosine and tangent ratios?
There aren't. There are three: Sine, Cosine and Tangent, for any given right-angled triangle. They are related of course: for any given angle A, sinA/cosA = tanA; sinA + cosA =1. As you can prove for yourself, the first by a little algebraic manipulation of the basic ratios for a right-angled triangle, the second by looking up the values for any value such that 0 < A < 90. And those three little division sums are the basis for a huge field of mathematics extending far beyond simple triangles into such fields as harmonic analysis, vectors, electricity & electronics, etc.
How does geometric properties help you find the value of trigonometric functions?
Geometric properties, particularly those related to right triangles and the unit circle, provide a visual framework for understanding trigonometric functions. In a right triangle, the ratios of the lengths of the sides (opposite, adjacent, and hypotenuse) directly define sine, cosine, and tangent. Similarly, on the unit circle, the coordinates of points correspond to the values of these functions for different angles, allowing for easy calculation of sine and cosine values. Thus, geometric insights simplify the evaluation and interpretation of trigonometric functions.
How are ratios for sin and cosine alike?
sin(x) = cos(pi/2 - x). Thus sine is simply a horizontal translation of the cosine function. NB: angles are measured in radians.
What trigonometric ratios cannot be greater than one?
Sine and cosine.
What are the units of sin cosine and tangent?
All three are ratios which do not have units.
What are trig ratios?
Trig ratios or to give them their proper name are trigonometrical rations applicable to right angle triangles and they are tangent ratio, sine ratio and cosine ratio.
How is sine and cosine different?
Sine and cosine are both trigonometric functions that relate to angles in a right triangle, but they represent different ratios. The sine function, denoted as sin(θ), gives the ratio of the length of the opposite side to the hypotenuse, while the cosine function, denoted as cos(θ), gives the ratio of the length of the adjacent side to the hypotenuse. In the unit circle, sine corresponds to the y-coordinate and cosine corresponds to the x-coordinate of a point on the circle at a given angle. This fundamental difference leads to distinct properties and applications in various fields such as physics, engineering, and mathematics.
How do you write ratios for sin and cosine?
sin = opp/hyp cos = adj/hyp tan = opp/adj
What is the introduction of plane trigonometry?
It starts with the simple Right-Angled Triangle and its 3 simple ratios: Sine, Cosine, Tangent...
What is the equation for finding the sine and cosine and tangent of a triangle?
For finding the angles in a right angled triangle the ratios are: sine = opposite divided by the hypotenuse cosine = adjacent divided by the hypotenuse tangent = opposite divided by the adjacent
What are trigometric ratios?
The ratios pertaining to right angled triangles are called trigonometrical ratios.They are- sine x = Opposite side/Hypotenuse cosine x= Adjacent side/Hypotenuse tangent x= Opposite side/Adjacent side Cosecant x= Hypotenuse/Opposite side secant x= Hypotenuse/Adjacent side cotangent x= Adjacent side/Opposite side Here, x is one of the angles in the trangle except the right-angled one.
What are the 3 basic trig ratios and how do they work?
The three basic ratios are sine, cosine and tangent.In a right angled triangle,the sine of an angle is the ratio of the lengths of the side opposite the angle and the hypotenuse;the cosine of an angle is the ratio of the lengths of the side adjacent to the angle and the hypotenuse;the tangent of an angle is the ratio of the lengths of the side opposite the angle and the the side adjacent to the angle.
What are the formula of trigonometry till class 10th?
Different topics are taught in different countries at various ages.I expect that the main formulae will be the definitions of sine and cosine ratios in the context of right angled triangles, the tangent ratio - either from a right angled triangle or in as derived from sine and cosine. There will also be the squared ratios identity. In year 10 or 11, pupils will learn the sine and cosine rules for general (non-right angled) triangles, and the area of a segment of a circle.
What does socotoa mean?
"SOHCAHTOA" is a mnemonic device used to remember the trigonometric ratios of sine, cosine, and tangent in right-angled triangles. The acronym stands for Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, and Tangent=Opposite/Adjacent.
