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12345 [234]
3 years ago
5

How do I do 2 and 3

Mathematics
2 answers:
german3 years ago
6 0

Answer:

y=52

x=46

questions 3

x=84

y=84

Step-by-step explanation:

ASHA 777 [7]3 years ago
4 0

Answer:

#2:   x = 64      y = 32\sqrt{3}

#3:   x = 6\sqrt{2}      y = 6\sqrt{2}

Or, if you are supposed to write your answers in decimal form instead:

#2:   x = 64      y = 55.43

#3:   x = 8.49      y = 8.49

Step-by-step explanation:

Special right triangles have specific angle measurements that tell you the lengths of each side. I attached an image that explains the rules of different special right triangles in case you need it :)

#2 is a 30-60-90 triangle. This means that <em>x</em> (the side opposite the 90° angle) is two times the length of the shortest side (32×2), and <em>y</em> is equal to 32\sqrt{3}.

#3 is a 45-45-90 triangle. This means that <em>x</em> (the side opposite the 45° angle) is equal to <em>y</em> (the side opposite the other 45° angle). The hypotenuse, 12, is x\sqrt{2} (or y\sqrt{2}, since x = y). This means 12 = x\sqrt{2}

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Graph the inverse circular function by hand, given f(x) = 3sin(2x) ;-pi/4 ≤ ≤pi/4
nasty-shy [4]

Part a)

a) The given function is

f(x) = 3 \sin(2x)

We let

y =  3 \sin(2x)

Interchange x and y.

x=  3 \sin(2y)

Solve for y;

\frac{x}{3}  =  \sin(2y)

y =  \frac{1}{2}  { \sin}^{ - 1}( \frac{x}{3} )

{f}^{ - 1}(x)  =  \frac{1}{2}  { \sin}^{ - 1}( \frac{x}{3} )

Part b) The range of f(x) refers to y-values for which f(x) exists.

The range of f(x) is

-  3 \leqslant y \leqslant 3

This is because the function is within y=-3 and y=3.

c) The range of

{f}^{ - 1} (x)

is

-  \frac{ \pi}{4}  \leqslant y \leqslant  \frac{\pi}{4}

The domain is -3≤x≤3

This is because the domain and range of a function and its inverse swaps.

Part d) The graph is shown in the attachment.

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