tan 45 gives me 0.9999

Question

Why does tan 45(0.7853981633974483 in radian) give me 0.9999? What's wrong with the following code?

System.out.println(Math.tan(Math.toRadians(45.0)) );

I don't think there's any typo in here.

So what's the solution here?

Answer 1

Floating point calculations will often lead to such inaccuracies. The problem is that numbers cannot be accurately represented within a fixed number of bits.

To give you another example (in decimal), we all agree that 3 * (1/3) = 1. However, if your calculator only has 4 decimal places, 1/3 would be represented as 0.3333. When that's multiplied with 3, you would get 0.9999 not 1.

As further information, floating points on most systems are usually represented using the IEEE754 standard. You could search for it, or refer the Wikipedia page for more details. IEEE floating point

Answer 2

The closest double to pi/4 is exactly 0x1.921fb54442d18p-1. The tangent of this double, to more bits than you need, is 0x1.fffffffffffff72cece67p-1. Rounding to the nearest double gives you exactly 0x1.fffffffffffffp-1 because 0x1.fffffffffffff72cece67p-1 is less than 0x1.fffffffffffff8p-1.

Answer 3

Use this

double radians = Math.toRadians(45.0);

System.out.format("The tangent of 45.0 degrees is %.4f%n", Math.tan(radians));