Step-by-step explanation:
why would you joke I was willing to help you hun but enjoy the rest of your day
Answer:
a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]
Step-by-step explanation:
a.We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Adding both equations, we have
e^jθ = cosθ + jsinθ
+
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ
Simplifying, we have
e^jθ + e^(-jθ) = 2cosθ
dividing through by 2 we have
cosθ = ¹/₂[e^jθ + e^(-jθ)]
b. We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Subtracting both equations, we have
e^jθ = cosθ + jsinθ
-
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)
Simplifying, we have
e^jθ - e^(-jθ) = 2jsinθ
dividing through by 2 we have
sinθ = ¹/₂[e^jθ - e^(-jθ)]
Assuming it's for a polynomial function, this video explains a lot https://www.youtube.com/watch?v=OrLz7yide2g hope this helps:)
Answer: B) Dilate by scale factor of 2
====================================================
Explanation:
Your teacher isn't saying this directly, but I'm assuming s/he wants you to find a similar figure that isn't congruent to the original. Informally, your teacher seems to want you to find a figure that is the same shape but not the same size as the original.
If so, then any dilation will shrink or enlarge the image depending on the scale factor. So the new image will not be the same as the old one. In this case, a dilation with scale factor 2 means the new figure is twice as large (each side is twice as long). But the old image is similar to the new image. The angles keep their values and therefore we get the same shape. This is why choice B is the answer. Again this is assuming what I mentioned in the first paragraph.
Choices A, C, and D are all known as rigid transformations and they preserve the same size of the figure. Applying any of those operations will lead to the same figure (just rotated, reflected or shifted somehow). In other words, applying operations A,C, or D will have us get two congruent triangles. If two triangles are congruent, then they are automatically similar, but not vice versa. This is why we can rule out A,C, and D.
