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In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle)
1) A reflection y = x followed by a rotation through pi
2) A reflection in y = -x
3) A reflection in the x axis followed by a rotation in the y axis
4) A rotation through -pi / 2 followed by a reflection in the y axis.
In each case, give the corresponding related angle formulas involving cos & sin.
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Angles are caluclated based transformations of trigonometric point, P(X). The solution is detailed and well presented.
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In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result
from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle)
1) A reflection y = x followed by a rotation through
Solution. If we only consider the points on the unit circle, so we can assume the coordinate of the original point is , then its reflection point, denoted by Q(x',y'), then follwed by a rotation ...
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
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