Answer:
Step-by-step explanation:
70 = x/4
x = 4 cos 70 = 1.37m
x = 4 cos 80 = 0.69m
The range is ( 0.69m, 1.37m)
(a) both a relation and a function
<u>Step-by-step explanation:</u>
In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain, and the set of all y-values is called the range. We must have a value of y for a value of x and so it's a relation.
Here , y = x/3 for every value of x we have a value of y as at x=1 we have y=1/3. So, it is a relation. Now, Relation is function when it passes vertical line test i.e. when we draw graph of y if we sketch many distinct vertical lines they all must cut graph at only one point and so its function. Basically, for every value of x we must have only one value of y. Y = x/3 follows the above rule and so its also a function! ∴ y=x/3 is both a relation & a function.
A mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
