Use the first five terms of the trigonometric series to find the value of sin pi/12 to four decimal places.
a. 0.2618
b. 0.2588
c. 0.7071
d. 0.2648
I got B, is this right?
Correct
To find the value of sin(pi/12) using the first five terms of the trigonometric series, you can use the Taylor series expansion for sine:
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
The first five terms of the series are:
sin(x) ≈ x - (x^3)/3! + (x^5)/5! - (x^7)/7!
Now, substitute x = pi/12 into the series:
sin(pi/12) ≈ (pi/12) - [(pi/12)^3]/3! + [(pi/12)^5]/5! - [(pi/12)^7]/7!
Carrying out the calculations, we get:
sin(pi/12) ≈ 0.2588190451
To four decimal places, this value is approximately 0.2588.
So, the correct answer is b. 0.2588.
Therefore, you are right.