How many algorithms are there to calculate exact values of Trigonometric ratio (sin, cos, tan) of any angle without using the value of pi?
Answers
Answer:
Step-by-step explanation:
Yes, you can calculate trigonometric functions without a calculator or table. The most straight-forward way is to use the MacLaurin series, which is usually given as the definition of sin and cos in most post-highschool textbooks:
sin(x)=x−x33!+x55−x77!+…
cos(x)=1−x22!+x44!−x66!+…
where n! denotes the factorial, i.e. the product of all positive integers up to n. Any real calculation naturally has to be of a finite truncation of the series, but we can approximate the real value that way with arbitrary precision by adding terms. We will need less terms if x is closer to 0.
Needless to say, these calculations can be quite tedious. Usually, computers look up the required value in a table (using linear interpolation if necessary), which is much more efficient.