Answer:
The values of x is -30 degrees and undefined
None of these values fall within the given range
Thus, no value within the given range is the solution to the equation
Step-by-step explanation:
Here, we want to find the value of x that works for the equation in the selected range
2cot^2x = -3csc x
Mathematically, from trigonometry;
cot^2x = csc^2x - 1
Substitute this above
2(csc^2x - 1)= -3csc x
let csc x = b
2(b^2-1) = -3b
2b^2 - 2 + 3b = 0
2b^2 + 3b - 2 = 0
2b^2 + 4b - b - 2 = 0
2b(b+ 2) - 1( b + 2) = 0
(2b-1)(b + 2) = 0
2b = 1
b = -2
b = 1/2 = 0.5
or b = -2
Recall;
csc x = b
x = csc^-1 b
x = csc^-1 0.5
x = undefined
Secondly;
b = -2
x = csc^-1 (-2)
x = -30 degrees
As we can see , between the points
0 ≤ x < 360
None of our answers fall in these range
Answer:
1. (4, 3) and (8, 6)
2. Yes. The line shows a direct proportion. y = 0.75x
Try (20, 15) in the equation.
15 = 0.75(20)
15 = 15
Point (20, 15) works in the equation, so point (20, 15) is on the line.
3.
Let x = 100.
y = 0.75x
y = 0.75 × 100
y = 75
Since x = 100 gives y = 75, point (100, 75) is on the line.
4.
Let x = 90
y = 0.75x
y = 0.75 × 90
y = 67.5
For x = 90, y must be 67.5. Since this point is (90, 68), it is not on the line.
We are given
Angles α and β are angles in standard position
and
α terminates in Quadrant II
β terminates in Quadrant I
and we have
we can use triangle and find cos(α)
we get
and we have
we can draw triangle
now, we can use formula
now, we can plug values
now, we can simplify it
...............Answer
Since none of the terms have the same variables the like terms would be (A) because they are both constants
