Basic Trigonometry and Vector Functions for PHY 100
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 I would like for you to know sine, cosine, and tangent for the angles of θ = 0, 30, 45, 60, and 90.


sin(θ) = Y/R

cos(θ) = X/R
tan(θ) = Y/X

R2 = X2 + Y2
R = √
(X2 + Y2)

 

sin(0) = 0.0
cos(0) = 1.0
tan(0) = 0.0
sin(30) = 0.5
cos(30) = 0.866
tan(30) = 0.577
sin(45) = 0.707
cos(45) = 0.707
tan(45) =
1.0
sin(60) = 0.866
cos(60) = 0.5
tan(60) = 1.732
sin(90) = 1.0
cos(90) = 0.0
tan(90) =

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 = X + Y

X = R cos(θ)
Y = R sin(θ)

R = |R|
X = |X|
Y = |Y|

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 R2 = X2 + Y2, we have R = (X2 + Y2) = (52 + 8.662) = (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.  

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