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: B, $78
Step-by-step explanation:
If the tip is 20% of the dinner cost, then we have to first find what is 20% of 65.
20% x 65 = 13. So the tip for the dinner is 13 dollars.
Now we have to add it to the original dinner cost.
65 + 13 = 78.
Therefore, the total cost of their meal is 78 dollars. So the answer is B, $78!
Answer:
I don't know ur Language .......
1. 20 cm by 20 cm by 6 cm
2. 40 cm by 30 cm by 2 cm
Hope this helps
<h2>
The circumference of small size, medium size and large size of pizzas are 25.12 inches, 31.4 inches and 37.68 inches.</h2>
Step-by-step explanation:
Given,
The diameter of small pizza = 8 inches,
The diameter of medium pizza = 10 inches and
The diameter of large pizza (d) = 11 inches
To find, the circumference of each size of pizza = ?
We know that,
The circumference of the circle = 
∴ The circumference of small size of pizza = 3.14 × 8 = 25.12 inches
The circumference of medium size of pizza = 3.14 × 10 = 31.4 inches
Also,
The circumference of large size of pizza = 3.14 × 12 = 37.68 inches
Thus, the circumference of small size, medium size and large size of pizzas are 25.12 inches, 31.4 inches and 37.68 inches.
You can also refer:
https://brainly.ph/question/1009095
