I calculated tan and sin (theta) for a physics lab experiment -- two-slit interference

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

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)

To find the percent error when you replace sin(theta) with tan(theta), you can compare the values obtained using both equations.

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%.