Find The Value Of (Sin 31) Using Approximation ?
well, it depends on how accurate you wish. You know the sine of 30 degrees from memory, 1/2 .
If you want it more accurately,
sin(30+1)sin30cos1+ cos30*sin1
well, convert 1 degree to radians, approximately 1/60=.016
sin(30+1)=.5+.016=.516
and my calculator says it is .515
that assumes that cos1 appx=1, and sin.016appx=.016
To find the value of sin 31 using approximation, you can use a calculator or a mathematical table. However, I can provide you with an approximate value.
Using a calculator, the value of sin 31 is approximately 0.515.
Please note that this is an approximate value and may not be exactly accurate.
To find the value of sin 31 using approximation, you can follow these steps:
Step 1: Convert the angle from degrees to radians.
To find the value of sin 31, first convert the angle from degrees to radians. Multiply the angle by π/180, where π (pi) is approximately 3.14159 and 180 is the number of degrees in a circle.
31 × π/180 ≈ 0.5411 radians (rounded to four decimal places).
Step 2: Use the Taylor series expansion.
The Taylor series expansion for sin(x) is:
sin(x) ≈ x - x^3/3! + x^5/5! - x^7/7! + ...
Using the first few terms of the series expansion will give us an approximate value for sin 31:
sin 31 ≈ 0.5411 - (0.5411)^3/3! ≈ 0.5221 (rounded to four decimal places).
Therefore, the approximate value of sin 31 is approximately 0.5221.