created Jan 14, 2020
Most programming exercises from other chapters could be improved by using printf()
in place of the usual println()
.
See also the exercises for chapter 14 which can be done without reading that chapter.
1. A fact from calculus is that
(1 + 1/x)x
gets closer and closer the the value 2.71828... as x
gets larger and larger.
This value is so useful in math that it has a name: e
.
It is the base for natural logarithms.
(But don't worry: you don't need to do math to write this program.)
Write a program that calculates this value for an x
entered by the user.
Enter x: 40000 Approximation to e: 2.7182479
x
gets very large before e
gets close to its true value.
To raise val
to a power, import java.lang.Math
and use
Math.pow( val, power )
which takes double precision arguments and returns a double precision value
2. Everyone's favorite trig identity is
sin( θ )2 + cos( θ )2 = 1
In math books this is usually written
sin2( θ ) + cos2( θ ) = 1
Write a program that demonstrates this. Prompt the user for an angle in degrees, then print out the sum of the two squares.
Input an angle: 37.5 sin(37.50) is: 0.61 cos(37.50) is: 0.79 sin(37.50)^2 is: 0.37 cos(37.50)^2 is: 0.63 sum is: 1.00
A problem is that Math.sin( rad )
and Math.cos( rad )
expect angles in radians.
There are 360 degrees in a circle and 2π radians in a circle.
To convert an angle from degrees to radians, multiply degrees by 2π/360.
Another way to do this is with:
Math.toRadians(deg)
To square a value, multiply it by itself (using *). Using Math.pow() is unneeded complication for squaring.
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