Can someone pls tell me how to do this?
1 answer:
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Answer:
The graph f(x)= is a reflection over the x-axis, vertical stretch by a factor of 2, a horizontal translation left 3 units and a vertical translation 4 units down of the graph y=
.
Step-by-step explanation:
The graph f(x) is reflected over the x-axis because the negative is outside of the parenthesis.
it's a vertical stretch by a factor of 2 because 2 is outside of the parenthesis and is greater than 1.
(x+3) is a horizontal translation left 3 units because it is inside the parenthesis.
-4 is vertical translation 4 units down because it is outside of the parenthesis.
The solutions appear to be {π/2, 2π/3, 4π/3}.
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}