Trigonometric Ratio Calculator

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Trigonometry is mathematical concept that deals with triangles, particularly right angle triangles. Trigonometry ratio calculator used to explain the relationships between the sides and angles of the triangles. We can also say that, the Brach math Trigonometry is math study of how the sides and angles of a triangle are related to each other. There are six ratios in the trigonometric. By using the trigonometric ratio calculator we can find the unknown value of the sides of the right angle triangle. Let us discuss about trigonometric ratio calculator and the problems related to trigonometric ratio calculator.

Trigonometric ratio:

Consider the following right angle triangles,

ratio

Fig (i) Right angle triangle

In the above figures,according to the angle x , the Adjacent side and Opposite side will be vary.

The following are the trigonometric ratio,

Sin x = (Opposite side)/ (Hypotenuse)

Cos x = (Adjacent side) / (Hypotenuse)

Tan x = (Opposite side) / (Adjacent side) = (sin x)/( cos x )

Inverase trigonometric Ratios:

Cosec x = (Hypotenuse) / (Opposite ...
... side ) = 1/(sin x)

Sec x = (Hypotenuse) / (Adjacent side) = 1 / (cos x)

Cot x = (Adjacent side) / (Opposite side) = 1/ (tan x) = (cos x /sin x)

Problems on trigonometric ratio:

Problem 1:

Find the ratio of sin ,cos,tan ,cosec,sec and cot for the following figure.

hngh

Solution:

sin x = AB /BC = 3/5

Cos x = AC/BC = 4/5

Tan x = AB/AC = 3/4

Cosec x = BC/AB = 5/3

Sec x = BC/AC = 5/4

cot x = AC/AB = 4/3

Problem 2:

Find the angles x and y and side a of the following triangle by using the trigonometric ratio calculator

fdf

Solution:

By using the pythagorean theorem we can find the side a of the triangle,

we know that, a = sqrt(b^2+c^2)

= sqrt(21^2+28^2)

= sqrt(1225)

= 35

Now we are going to find the angls x and y by using the sin ratio.

Sin x = opposite side /Hypotenuse = 21/35

sin x = 0.6

Taking sin inverse on both side,

x = sin-1 (0.6)

x = 36.87 degree

Sin y = opposite side /Hypotenuse = 28 /35

sin y = 28 /35 = 0.8

Taking sin inverse on both side,

y = sin-1 (0.8)

y = 53.13 degree.

Answer: x = 36.87 degree

y = 53.13 degree

a = 35

Verification:

To check the answer Apply the following rule,

The total sum of the angles is equal to 180 degree.

36.87+53.13 + 90 = 180

We get the sum of the angles is 180 degree.So the answer is correct.

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Let we learn about geometric mean calculator. The geometric mean should be a type of mean. Which represents central tendency or typical value of set of numbers. This is similar to arithmetic mean calculator. This is the process that except numbers are multiplied and then the nth root of resulting product. Here, n is count of numbers in the set.

More about geometric mean calculator:

The geometric mean could be understood in provisions of geometry.

Geometric mean calculator of two numbers:

Let two numbers p and q should be length over one side of square.
Their area = Area of a rectangle with sides of lengths c and d.

Geometric mean calculator of three numbers:

Let us consider the numbers be a, b, and c.
Here, the geometric mean will be the length over a side of cube.
Whose volume should be same as cuboid with sides.
Whose lengths = Given three numbers.

Calculation:

Let us consider a data set [a1, a2, ..... an ]
Geometric mean of that data set will be,

\bigg(\prod_{i=1}^n a_i \bigg)^{1/n} = \sqrt[n]{a_1 a_2 \cdots a_n}.

Geometric mean of a data set