Basic Trigonometry and Vector Functions for PHY 100
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Examples:
4 x cos(30°) = 4 x 0.866 =
3.464
1 / sin(30°) = 1 / 0.5 = 2.0
cos(45°) / sin(45°) = 0.707 /
0.707 = 1.0
Vectors:
So, if R is a vector, then R is the sum of vectors X
and Y. That is
R = R 
Examples:
1)
A vector with magnitude 10m at 60°. What are the magnitudes of the
components or rather the lengths of the legs?
Answer:
X = 10m x cos(60°) =
10m x 0.5 = 5m
Y = 10m x sin(60°) = 10m x 0.866 = 8.66m
2) If the components of a vector are
X = 5m and Y = 8.66m, what is the magnitude of the vector?
Answer:
Using R^{2} = X^{2} + Y^{2}, we have R = √(X^{2} +
Y^{2}) = √(5^{2} + 8.66^{2})
= √(25 + 75) = √100
= 10m (rounding off)
3) A vector at 45° has a magnitude
of 35m. What is the vertical Y component?
Answer:
Y = R x sin(45°) = 35 x 0.707 = 24.7 m (also, the X
component would be 35 x cos(45°) = 35 x 0.707 = 24.7)
The above is the level of trigonometry and vectors that we will use in PHY 100. In other words, I will ask questions that are only in angles of 0°,30°,45°,60°, and 90°. You can use a calculator to determine the angles or you can use the table above, whichever is comfortable for you.