Contents
What is the correlation between sin and cos?
Sal shows that the sine of any angle is equal to the cosine of its complementary angle.
How do you know if sin and cos graphs are apart?
In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.
How is the correlation coefficient related to covariance?
The correlation coefficient is a dimensionless metric and its value ranges from -1 to +1. The closer it is to +1 or -1, the more closely the two variables are related. If there is no relationship at all between two variables, then the correlation coefficient will certainly be 0.
How to calculate the correlation between sine and cosine?
Let Y = sinX and Z = cosX. Show that the correlation between Y and Z is zero. It seems I would need to know the standard deviation of the sine and cosine, and their covariance. How can I calculate these? I think I need to assume X has uniform distribution, and the look at the transformed variables Y = sin(X) and Z = cos(X).
Why is covariance zero in case of independent variables?
Covariance is zero in case of independent variables (if one variable moves and the other doesn’t) because then the variables do not necessarily move together. Independent movements do not contribute to the total correlation. Therefore, completely independent variables have a zero correlation.
How to calculate the covariance of X and Y?
The covariance of (X, Y) is defined by cov(X, Y) = E([X − E(X)][Y − E(Y)]) and, assuming the variances are positive, the correlation of (X, Y) is defined by cor(X, Y) = cov(X, Y) sd(X)sd(Y) If cov(X, Y) > 0 then X and Y are positively correlated. If cov(X, Y) < 0 then X and Y are negatively correlated. If…