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)]
Answer:
All 3 angles are the same, it is simply a dilation. the size is the only difference.
Step-by-step explanation:
You are correct with 80 on that answer. because since it is a polygon all sides add up to 180. you take 180 and subtract the number u have which is 100. u can double check your answer by looking at the angle. by looking its definitely less than 90 and not more than 90. it looks 80 to me and you can prove it by doing this 180-100=80
ANSWER=80°
Answer:
-0.5, negative 1 over 5, 1 over 9, 1
Step-by-step explanation:
Hope this helps! :) please mark me as brainly :)
Answer:
60-2x=v
Step-by-step explanation: