Root of any degree Root(n, x)

Notation:
Root(n, x), where
n – redicand
x – index
x, n – any numbers or expressions.
For an even root, the redicand cannot be negative.

Examples:
Cubic root of fraction 2/5
Root(2/5, 3)

Other examples
Root(1.5, 3)
Root((3*5), 3/2)
Root(1.5, 3/7)

Exponentiation Pow(n, x)

Notation:
Pow(n, x), where
n – base
x – exponent or power
x, n – any numbers or expressions.

Examples:
Five to the power of three
Pow(5, 3)

Other examples
Pow(12.5, 3)
Pow((3-5), 3/2)
Pow(1.5, Sqrt(2))

Logarithm Log(n, x)

Notation:
Log(n, x), where
n – the number whose logarithm you want to find
x – base.
x > 0, x ≠ 1, n > 0

Examples:
Log5 34 (logarithm of 34 to base 5), should be written as
Log(34, 5)

Natural logarithm Ln(n)
The base is equal to Euler's number e
(e = 2.7182818284...)

Notation:
Ln(n), where
n > 0<

Examples:
Ln(7)

Common logarithm Lg(n)
The logarithm base 10

Notation:
Lg(n), where
n > 0

Examples:
Lg(1.6)

Binary logarithm Lb(n)
The logarithm base 2

Notation:
Lb(n), where
n > 0

Examples:
Lb(3/6)

Greatest common divisor Gcd(n, m)

Notation:
Gcd(n, m), where
n, m – non-negative integers

Examples:
Gcd(12; 16) should be written as
Gcd(12, 16)

Least common multiple Lcm(n, m)

Notation:
Lcm(n, m), where
n, m – non-negative integers

Examples:
Lcm(4; 23) should be written as
Lcm (4, 23)

Trigonometric functions
All trigonometric functions take one or two arguments. If the function takes one argument, then the number is considered to be in radians.

Sine of an angle Sin(x)

Notation:
Sin(x)
Sin(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Sine π/3 radians
Sin(π/3) or Sin(π/3, Rad)

Sine 60° degrees
Sin(60, Deg)

Cosine of an angle Cos(x)

Notation:
Cos(x)
Cos(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cosine π/3 radians
Cos(π/3) or Cos(π/3, Rad)

Cosine 60° degrees
Cos(60, Deg)

Tangent of an angle Tan(x)

Notation:
Tan(x)
Tan(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Tangent π/3 radians
Tan(π/3) or Tan(π/3, Rad)

Tangent 60° degrees
Tan(60, Deg)

Cotangent of an angle Cot(x)

Notation:
Cot(x)
Cot(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cotangent π/3 radians
Cot(π/3) or Cot(π/3, Rad)

Cotangent 60° degrees
Cot(60, Deg)

Secant of an angle Sec(x)

Notation:
Sec(x)
Sec(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Secant π/3 radians
Sec(π/3) or Sec(π/3, Rad)

Secant 60° degrees
Sec(60, Deg)

Cosecant of an angle Csc(x)

Notation:
Csc(x)
Csc(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Cosecant π/3 radians
Csc(π/3) or Csc(π/3, Rad)

Cosecant 60° degrees
Csc(60, Deg)

Inverse trigonometric functions
All inverse trigonometric functions take one or two arguments. If the function takes one argument, then the function will return the solution in radians.

Arcsine Asin(x)

Notation:
Asin(x)
Asin(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsine 1/3 (get the solution in radians)
Asin(1/3) or Asin(1/3, Rad)

Arcsine 1/3 (get the solution in degrees)
Asin(1/3, Deg)

Arccosine Acos(x)

Notation:
Acos(x)
Acos(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arccosine 1/3 (get the solution in radians)
Acos(1/3) or Acos(1/3, Rad)

Arccosine 1/3 (get the solution in degrees)
Acos(1/3, Deg)

Arctangent Atan(x)

Notation:
Atan(x)
Atan(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arctangent 1/3 (get the solution in radians)
Atan(1/3) or Atan(1/3, Rad)

Arctangent 1/3 (get the solution in degrees)
Atan(1/3, Deg)

Arccotangent Acot(x)

Notation:
Acot(x)
Acot(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arccotangent 1/3 (get the solution in radians)
Acot(1/3) or Acot(1/3, Rad)

Arccotangent 1/3 (get the solution in degrees)
Acot(1/3, Deg)

Arcsecant Asec(x)

Notation:
Asec(x)
Asec(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsecant 1/3 (get the solution in radians)
Asec(1/3) or Asec(1/3, Rad)

Arcsecant 1/3 (get the solution in degrees)
Asec(1/3, Deg)

Arcsecant Acsc(x)

Notation:
Acsc(x)
Acsc(x, measure)
Where
x – number
measure – can take values Rad or Deg

Examples:
Arcsecant 1/3 (get the solution in radians)
Acsc(1/3) or Acsc(1/3, Rad)

Arcsecant 1/3 (get the solution in degrees)
Acsc(1/3, Deg)

Expressions containing multiple embedding of functions and mathematical operations
Any expression can contain other expressions, the limit on the length of an expression is 100 characters.

Examples:
Root(Pow(3, 6), 2);
(5/2-4)*34/5-(Root(3, 2))
(12-123+5)/(12.45*(34/6))
Sin(60, Deg)+Cos(45, Deg)
etc.

Time Calculator, if Known: Distance Traveled and Speed

Time is equal to the ratio of distance to speed.

Distance
Speed

Time Calculator, if Known: Acceleration and Speed

If initial speed v0 is zero, put zero in the field for initial speed v0

Initial speed v0
Final speed v
Acceleration a

Time Calculator, if Known: Acceleration, Speed and Distance Traveled

If speed velocity v0 is zero, put zero in the field for initial speed v0

Initial speed v0
Distance S
Acceleration a

Examples of Calculating Time if the Distance Traveled and Speed Are Known

Example 1.
The boat sailed 1736 yards at a speed of 60 Kilometers per hour. How long did the boat sail?

Step by step solution:
Convert yards to kilometers. One kilometer is 1093.61 yards, so we divide yards by 1093.61.
1736 : 1093.61 = 24800/15623 = 1.58740318760801 kilometers.

Find time, divide distance by speed.

Time =

	24800/15623
	60

= 1240/46869 = 0.0264567197934669 hours

Time = 0 hours 1 minutes 35.2441912564808 seconds

Example 2.
The car, moving at a speed of 12 yards per second, covered a distance of 3000 kilometers. How long did the car drive?

Step by step solution:
Converting kilometers to yards. One kilometer is 1093.61 yards, so multiply kilometers by 1093.61.
3000 × 1093.61 = 3280830 yards.

Find time, divide distance by speed.

Time =

	3280830
	12

= 546805/2 = 273402.5 seconds

Time = 75 hours 56 minutes 42.5000000000091 seconds

Examples of calculating the time, if the acceleration and speed are known for a uniformly accelerated rectilinear motion

Example 1.
The aircraft moved uniformly accelerated with an acceleration of 25000 km/h². Before takeoff, the aircraft's speed increased from 15 to 100 m/s². Determine the time during which the airplane's speed increased from 15 to 100 m/s².
Step by step solution:

Convert meter per second to kilometer per hour.

Let's convert meters to kilometers. There are 1000 meters in one kilometer, so we divide the meters by 1000.
15 : 1000 = 3/200 = 0.015 kilometers.

Let's convert seconds to hours.
There are 3600 seconds in one hour, so we need to divide the number of seconds by 3600.
1 : 3600 = 1/3600

Divide distance by time

v₀ =	3/200
	1/3600

= 54 Kilometers per hour

Convert meter per second to kilometer per hour.

Let's convert meters to kilometers. There are 1000 meters in one kilometer, so we divide the meters by 1000.
100 : 1000 = 1/10 = 0.1 kilometers.

Let's convert seconds to hours.
There are 3600 seconds in one hour, so we need to divide the number of seconds by 3600.
1 : 3600 = 1/3600

Divide distance by time

v =	1/10
	1/3600

= 360 Kilometers per hour

Let's find the time, divide the difference between the final and initial speeds by acceleration.

t =

	360 - 54
	25000

= 153/12500 = 0.01224 hours

Time = 0 hours 0 minutes 44.064 seconds

Examples of calculating the time, if the acceleration, speed and distance traveled are known for a rectilinear uniformly accelerated motion

Example 1.
The cyclist, moving with a constant acceleration of 0.5 m/s² and an initial speed of 30 km/h, drove down the mountain. Calculate the time taken by the cyclist to descend if the length of the slide was 120 meters.
Step by step solution:

Convert kilometer per hour to meter per second

Let's convert kilometers to meters. There are 1000 meters in one kilometer, so we multiply kilometers by 1000.
30 × 1000 = 30000 meters.

Let's convert hours into seconds.
There are 3600 seconds in one hour, which means we need to multiply the number of hours by 3600.
1 × 3600 = 3600

Divide distance by time