For small angles, sin theta is approximately equal to tan theta = Y/L
= 0.25/2
Calculate the error (0.25/2.01 - 0.25/2)/(0.25/2.01)
I had to use this equation y = L tan (theta), with
y = 0.25 and L = 2 and tan (theta) came out to be 7.12 in degrees and 0.1243 in radians.
I found sin (theta) by using the triangle for
X^2 + Y^2 = R^2
Sin (theta) (0.25/2.01) = 7.14 in degrees and 0.1246 in radians.
Now, I have to find the percent error made when you replace the sin by the tangent leading to this equation
d(Y/L) = nλ, or
Y/n = (L/d)λ
I don't know how to do this, I'm extremely confused
= 0.25/2
Calculate the error (0.25/2.01 - 0.25/2)/(0.25/2.01)
Let's first calculate the value obtained using the original equation:
sin(theta) = 0.25/2.01 = 0.1246 radians
Now, let's calculate the value obtained using the tangent equation:
tan(theta) = 0.1243 radians
To find the percent error, we'll use the formula:
Percent error = ((Obtained Value - Actual Value) / Actual Value) * 100
However, in this case, we do not have the actual value to compare with. So, we'll assume that the obtained value using the original equation is the actual value.
Percent error = ((tan(theta) - sin(theta)) / sin(theta)) * 100
Percent error = ((0.1243 - 0.1246) / 0.1246) * 100
Now, let's calculate this using a calculator:
Percent error = (-0.0003 / 0.1246) * 100
Percent error ≈ -0.24% (rounded to two decimal places)
So, when you replace sin(theta) with tan(theta), the percent error is approximately -0.24%.