How to Find Sine of an Angle Without a Calculator

A calculator uses these basic operations to find the sine of an angle (+,-,\,x). It uses algorithms to find an approximation of sine. An algorithm is a precise set of rules and steps to perform a task. Taylor series is one of these algorithms to find the sine of an angle: sin x = x - x^3/3! + x^5/5! - x^7/7!.

Things You'll Need

• Scientific calculator

Instructions

1. Assume that the angle is 25 degrees. Taylor series works in radians so convert 25 degrees into radians by dividing 25 degrees by 180 degrees and you get .13889.

2. Now multiply this by pi, pi = (3.1459) So you get (.13889)x(3.1459)= .436332. This solution is x so that means x=.436332

3. Use 0.436332 as x in the formula and plug this value into each part of the equation: sin (.436332) = (.436332) - (.436332)^ 3/3! + (.436332)^5/5! - (.436332)^ 7/7!

4. Calculate the first value using a calculator: (.436332)^3/3! = (.083071)/(1x2x3)=.013845 note: 3! Is a factorial short for 1x2x3

5. Calculate with a calculator the second value in the series: (.436332)^ 5/5!= (.015815)/(1x2x3x4x5)=.015815/120=.000132. Note: 5! Is a factorial short for 1x2x3x4x5

6. Calculate the last value of the series: (.436332)^ 7/7!= (.003011)/(1x2x3x4x5x6x7)=.003011/5040=.000006. Note: 7! Is a factorial short for 1x2x3x4x5x6x7

7. Plug in all the values: sin .436332=.436332-.013845 +.000132-.000006=.422613 radians.

References

• Home School Math