Answer:
The point (0,-2) is the solution to the problem. Substitue 0 into x, the answer is -2 which matches f(x), or y value.
Step-by-step explanation:
The answer to the question
Answer:
X=1
Step-by-step explanation:
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:
square; perimeter 20 units; area 25 square units.
Step-by-step explanation:
As the attachment shows, each side of the polygon is the hypotenuse of a 3-4-5 right triangle, so has length 5 units. The perimeter is the sum of those lengths, 4×5 = 20; the area is the product of the lengths of adjacent sides, 5×5 = 25.
The figure is a square of side length 5 units.
The perimeter is 20 units; the area is 25 square units.
