Trigonometry

-3 + ln x = 5

Add '3' to boths sides

Hence ln x = 8

'ln' is logarithms to the natural base , which is 2.718281.... = 'e'

Hence log(e) x = 8

x = e^(8)

x = 2.71828...^8) = 2980.95798...

NB One the calculator you will find two buttons, viz. 'log' & 'ln'.

Log is logarithsm to base '10'

Ln is logarithms to base 'e' = 2.71828.... ( The exponential .

A 3d shape with 5 faces can be a square pyramid

Each bars height represents a certain number. Read all these heights and add the numbers together. Then take each individual bars value divide that by the total and multiply by 100 to get percentages.

The sine graph and the cosine graph are identical in shape, with the cosine graph shifted to the left by pi / 2, i.e. the sine starts at (x=0,y=0) and proceeds up with an initial slope of one, and the cosine starts at (x=0,y=1), and proceeds down with an initial slope of zero.

Coordinate planes are typically labeled with Roman numerals to distinguish between the horizontal axis (X-axis) and the vertical axis (Y-axis). Roman numerals are used as a traditional and standardized way to label the axes in mathematics to avoid confusion. This labeling convention helps to clearly identify the axes and their corresponding values when graphing points or plotting equations on the coordinate plane.

1. A cosine can be calculated as the length of the adjacent side divided by the length of the hypotenuse of a right angled triangle. The tangent measure is the length of the opposite side divided by the length of the adjacent side. As the cosx = 0.6 = 3/5 then we are dealing with a right angled triangle where the adjacent side measures 3 units and the hypotenuse 5 units - thus the opposite side measures 4 units as by Pythagoras' Theorem, 5² = 3² + 4². Then tanx = 4/3.

2. sin²x+cos²x=1.

sin² x=1-0.6²=0.64 and sin x=0.8.

tan x=sin x/cos x=0.8/0.6=8/6=4/3.

Well, darling, the value of tan(58.5 degrees) is approximately 1.612. So, if you're looking to impress someone with your trigonometry skills, go ahead and drop that little nugget of knowledge on them. Just don't expect them to be as impressed as they should be.

A good name for a maths magazine could be Q.E.D (It is very symbolic for a maths magazine).

The inverse tangent, denoted as arctan or tan^(-1), of 1.4737 is approximately 56.05 degrees when measured in degrees or approximately 0.980 radians when measured in radians. This value represents the angle whose tangent is 1.4737. In trigonometry, the inverse tangent function helps determine the angle when the tangent ratio is known.

Well, isn't that a lovely question! The value of tangent 37.5 degrees is approximately 0.7536. Just like painting a happy little tree, math can be a wonderful adventure full of surprises and beauty. Keep exploring and embracing the joy of learning!

Suppose the wall is represented by the y-axis and the ground as the x-axis. Let the position of the man be given by M = (x, y).

Then,

since M is the midpoint of the ladder, the base of the ladder is at A = (2x, 0).

also, the point where it touches the wall is B = (0, 2y).

Now, AB is the length of the ladder so AB = constant.

Using Pythagoras's theorem,

(2x - 0)2 + (0 - 2y)2 = c

(2x - 0)2 + (2y - 0)2 = c

This is the equation of [a quadrant of] a circle with centre (0, 0) and radius = sqrt(c).

It does not necessarily do so.

f(x) = cos(x + 2) will not start at 1.

1 in 10 to the 17th power is written as 1 x 10^17, which is equivalent to 1 followed by 17 zeros. In numerical terms, this is equal to 100,000,000,000,000,000. This number represents a very large quantity, often used in scientific notation to denote values in the realm of astronomy, physics, and other fields dealing with vast quantities.

Ah, a score is a beautiful way to say 20 units. Just like how we might paint 20 happy little trees in a landscape, a score is simply a group of 20 units all gathered together. So, when you hear the word "score," just imagine a lovely bunch of 20 units standing together, creating a harmonious number.

Sine (0) = 0

Sin(30) = 0.5

Sin(45) = 0.7071...

Sin(60) = 0.8660....

Sin(90) = 1

Are just a few of the Sine(Trigonometric) values.

Some key contributors to the development of trigonometry include ancient civilizations such as the Babylonians and Egyptians, who used rudimentary trigonometric concepts for practical purposes. The Greek mathematician Hipparchus is often credited with formalizing the field of trigonometry, introducing the trigonometric functions and developing the earliest trigonometric tables. Later, Islamic mathematicians such as Al-Battani and Al-Khwarizmi made significant advancements in trigonometry, further expanding its applications in astronomy, geography, and mathematics. These early pioneers laid the foundation for the modern study and application of trigonometry in various fields.

Sine is = to opposite side/hypotenuse,

using a triangle with sides of opposite ~ 1, adjacent ~ 1 and hypotenuse ~ root(2),

hypotenuse is always positive,

hypotenuse = root(adjacent.squared * opposite.squared)

if either is negative, squaring them brings it back to a positive

and as the opposite side is the rise from the base line ( 0 degrees through to 180 degrees) it is positive in both quadrants 1 and 2

in quadrant 1, sine= 1/root(2) which is positive

in quadrant 2, sine= 1/root(2) which is positive

in quadrant 3, sine= -1/root(2) which is negative

in quadrant 4, sine= -1/root(2) which is negative

so sine is positive in quadrants 1 and 2 and is negative in 3 and 4

Quadrant angles are the angle lies in different quadrants.

The angles which lie between 0° and 90° are said to lie in the first quadrant. The angles between 90° and 180° are in the second quadrant, angles between 180° and 270° are in the third quadrant and angles between 270° and 360° are in the fourth quadrant Quadrant angles are the angle lies in different quadrants.

The angles which lie between 0° and 90° are said to lie in the first quadrant. The angles between 90° and 180° are in the second quadrant, angles between 180° and 270° are in the third quadrant and angles between 270° and 360° are in the fourth quadrant

Well, honey, an acute triangle is any triangle where all three angles are less than 90 degrees. So, think of a slice of pizza or a traffic cone - those are acute triangles in the real world. Just keep your eyes peeled, acute triangles are everywhere, unlike a decent cup of coffee in a gas station.

Three earthquake detecting locations, usually the three closest seismographs all record a reading for how long it took the p then s waves to get there and how strong they are. With a compass, a circle or arc is created around each station depending on its distance from the epicenter based on the data. The point where the three circles intersect to create a triangle type figure is where the epicenter is. You can then connect the three stations into a triangle and get more accurate date from the side lengths and angles to the epicenter.

Well, isn't that a happy little math problem we have here! Let's see, the two prime numbers that add up to 78 are 41 and 37. Just like in painting, sometimes you need to mix different colors to create something beautiful. Happy calculating!

Steps:

1] Start

2] Initialize double sum=0,x,i,j,y,z=1,a,f=1,k=1;

3] Enter x //ie: The range of sin series

4] Read x

5] Repeat steps 6 to 11 for(i=1 to i<=x)

6] Set j=z=1

7] Repeat steps 8 while(j<=i)

8] Set z=z*i;j=j+1;

9] Repeat steps 10 while(k<=i)

10] Set f=f*k;k=k+1;

11] set a=z/f;sum=sum+a;

12] Display sum

13] Stop

Archaeologists use Trigonometry to divide up the excavation sites properly into equal areas of work. They can also use it to help them identify different tools used by the civilization are they are excavating. They can also use it to measure the distance from underground water systems near their dig site.