Nice vid. The manual ways of calculating angles is obsolete. The common angles were commited to memory like 30, 45, 60, 90 and integer multiples to 360 degrees. The functions were available in books of tables. The second way was to use the "slide rule". See: **broken link removed**
Interpolation had to be used to calculate values that were not in the table and is used today. Suppose you had the following table.
x y
1 4
2 8
If you wanted the value of 1.5, you could interpolate and get 6 for y. It's like noticing that 1.5 is 1/2 the distance between 2 and 1 and therefore the Y value is 1/2 the distance between 8 and 4 so you get 6.
Computers can do it using something called an "infinite series" (we are not going there) and micros could use a lookup table or an infinite series.
There is an identity that can help as well: [latex]sin(x)^{2}+cos(x)^{2}=1[/latex]
I won't take "interpolation" further than this unless you want to. It's easy.
Interpolation had to be used to calculate values that were not in the table and is used today. Suppose you had the following table.
x y
1 4
2 8
If you wanted the value of 1.5, you could interpolate and get 6 for y. It's like noticing that 1.5 is 1/2 the distance between 2 and 1 and therefore the Y value is 1/2 the distance between 8 and 4 so you get 6.
Computers can do it using something called an "infinite series" (we are not going there) and micros could use a lookup table or an infinite series.
There is an identity that can help as well: [latex]sin(x)^{2}+cos(x)^{2}=1[/latex]
I won't take "interpolation" further than this unless you want to. It's easy.
Last edited: