Quick trig which equation represents the graph of y = cos x flipped across the x-axis then shifted vertically up by 2 units?
y = -cos x + 2
y = -cos x - 2
y = cos(x - 2)
y = cos(-x) + 2

Step-by-step explanation:

Given :  y = cos x

To Find : Which equation represents the graph of y = cos x flipped across the x-axis then shifted vertically up by 2 units?

Solution :

y = cos x

Since we are given that the graph of y = cos x flipped across the x axis

So it will be lying in negative x axis

So, equation becomes y= - cos x

Now shift the obtain graph vertically up by 2 units

When the graph ships vertically up by some units so f(x) becomes f(x)+b

Where b is the units by which the graph shifts

Since the obtained graph is  f(x) = y = -cos x

So after the vertically upward shift by 2 units :

y = -cos x+2

Thus Option A is correct .

Refer the attached figure

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

the radius is 2 times the diameter.

step-by-step explanation: