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: 4,863.1
Step-by-step explanation:
Answer:
She will not meet her goal.
Step-by-step explanation:
There are 5 weekdays, so she will run for 0.5 * 5 = 2.5 hours over the weekdays
There are 2 weekends, so she will run for 2 * 1 = 2 hours over the weekend.
In total, this means she will run for 4.5 hours.
4.5 hours * 550 calories per hour = 2475 calories.
She will not meet her goal.
