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: 7
Step-by-step explanation:
7
You will have to use trig to solve this:
The side you have is adjacent to the known angle
The side you are looking for is opposite the known angle
^^^This means you need to use tan:
tan(24) = 
.445222 =
^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x
5.3 ≈ x
Hope this helped!
Answer:
chicken and chicken
Step-by-step explanation:
just took the test
Answer:
The smallest side is 7inches
Step-by-step explanation:
Let the shorter side be y.
The medium side is 4 more than the short side i.e
Meduim side = 4 + y
The longest side is 5 times the length of the shortest side i.e
Logest side = 5y.
Perimeter of the triangle = 53 inches
But the perimeter of a triangle is the Sum of all sides i.e
P = small + medium + large
53 = y + (4+y) + 5y
53 = y + 4 + y + 5y
Collect like terms
53 — 4 = 7y
49 = 7y
Divide both side by 7
y = 49/7
y = 7inches
Therefore the smallest side is 7inches
