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)]
10 5/12 can be turned into a improper fraction by multiplying 10 and 12. You get 120. Then you can add 5 and get 125/12.
THE ANSWER IS 125/12!
Answer:
The equation of the least-squares regression line for this plot is approximately ŷ = 3.8 + two thirds times x.
Step-by-step explanation:
God I remember when I had to that last year in 7th grade honors. I know you have to set up a proportion.
25/6. X/4. Find x and you get your answer
Answer:
using quaderatic expression solving problems of algebraic expressions.
Step-by-step explanation:
no1.
take the smallest side to be x
and the longest side to be x-1/3
then expand the expression equating to 30.
then solve for x value
