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4 years ago

Answer both questions please

Mathematics

1 answer:

olga_2 [115]4 years ago

4 0

I did the first one.
a. The equation that you need to get DF.
b. Substitute the values in the equation.
c. Add up the rs and the numbers (to simplify).
d. divide both sides by 5 to get r.
e. The value of r is given.

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Use your understanding of the unit circle and trigonometric functions to find the values requested.

vfiekz [6]

Answer:

a) For this case we can use the fact that $sin (\pi/3) = \frac{\sqrt{3}}{2}$

And for this case since we ar einterested on $-\frac{\pi}{3}$ and we know that the if we are below the y axis the sine would be negative then:

$sin (-\pi/3) = -\frac{\sqrt{3}}{2}$

b) From definition we can use the fact that $tan x= \frac{sin x}{cos x}$ and we got this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}$

We can use the notabl angle $\pi/4$ and we know that :

$sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}$

Then we know that $5\pi/4$ correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

Step-by-step explanation:

For this case we can use the notable angls given on the picture attached.

Part a

For this case we can use the fact that $sin (\pi/3) = \frac{\sqrt{3}}{2}$

And for this case since we ar einterested on $-\frac{\pi}{3}$ and we know that the if we are below the y axis the sine would be negative then:

$sin (-\pi/3) = -\frac{\sqrt{3}}{2}$

Part b

From definition we can use the fact that $tan x= \frac{sin x}{cos x}$ and we got this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}$

We can use the notabl angle $\pi/4$ and we know that :

$sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}$

Then we know that $5\pi/4$ correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

6 0

3 years ago

mr and mrs gracia took their three children to see a matinee on saturday. they spent a total of 55.50, which included 29.95 at t

andrezito [222]

First, you would subtract 29.95 from 55.50, and you get 25.55. because 5 people went, and the cost for each was the same, you would divide 25.55 by five, and get $5.11 per person.

3 0

3 years ago

If ab = 2, bc = 6 and ca = 3 then find the value of a.<br>

adelina 88 [10]

Answer:

a = 1

Step-by-step explanation:

5 0

3 years ago

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A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder. ...?

Kruka [31]

The volume of a cylinder can be calculated by the product of the area of the base times the height of the shape. It is expressed as follows:

V = πr²h

We calculate as follows:

320π in³= π (r²) (5 in)
64 in² = r²
r = 8 in

Hope this answers the question. Have a nice day.

4 0

3 years ago

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Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applie

adoni [48]

Answer:

Location of T' on the coordinate axis will be (16,7).

T (6,4) → T' (16,7).

Step-by-step explanation:

coordinate vertices of points in rectangle JKLM are:

J (-8,-8)

K (-4,-8)

L (-4,-5)

M (-8,-5)

and coordinate vertices of points in rectangle J'K'L'M' are:

J' (2,-5)

K' (6,-5)

L' (6,-2)

M' (2,-2)

coordinate vertices of points in Quadrilateral STUV are:

S (1,4)

T (6,4)

U (4,6)

V (2,6)

transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:

J (-8,-8) → J' (2,-5)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

similarly for

K (-4,-8) → K' (6,-5)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.

L (-4,-5) → L' (6,-2)

⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

M (-8,-5) → M' (2,-2)

⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.

and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.

So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:

along x axis the Quadrilateral will shift towards right by 10 units

So, 6 → 6+10=16

and along y axis the Quadrilateral will shift upwards by 3 units

So, 4 → 4+3=7

⇒ T (6,4) → T' (16,7).

7 0

3 years ago

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