Answer: It is a function
Why? Because it is impossible to draw a vertical line through more than one point on the red graph. Any vertical line will only pass through exactly one point on the red graph.
Put another way: any input x leads to exactly one and only one output y. If it was possible to have some input lead to multiple outputs, then it would be possible to draw a vertical line through more than one point on the red graph. The graph is said to "pass the vertical line test" proving it is a function.
note the closed circle at (0,2) and the open hole 2 units above that. If the open hole was filled in, then this is where the graph would fail the vertical line test; however, the open hole helps this piecewise graph be a function.
Answer:
349 is the answer.
Step-by-step explanation:
Answer:
1. 0, 2 π , π , 2 π/3 , 4 π/3
2. 7 π/6 , 11 π/6
Step-by-step explanation:
1. we want to find the value of theta
Let us represent theta by x for ease of documentation
So we have ;
sin 2x + sin x = 0
Mathematically;
sin 2x = 2sinxcosx
So;
2 sin x cos x + sin x = 0
sin x (2 cos x + 1) = 0
sin x = 0
or
2cos x + 1 = 0
x = arc sin (0)
within the given range;
x = theta = 0 , 2 π , π
For;
2 cos x + 1 = 0
2cos x = -1
cos x = -1/2
cos x = -0.5
x = arc cos (-0.5)
x = 2 π/3 , 4 π/3
2. cos 2 x = 1 + sin x
Mathematically;
cos 2 x = 1-2 sin^2x
let sin x = y
1-2y^2 = 1 + y
y = -2y^2
1 = -2y
y = -1/2
y = -0.5
sin x = y
sin x = -0.5
x = arc sin (-0.5)
x = 7 π/6 , 11 π/6
2 9/10 in decimal form would be,
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