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Eddi Din [679]
3 years ago
5

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

Mathematics
1 answer:
vfiekz [6]3 years ago
6 0

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

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ELEN [110]
2.1 x 4/0.5
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8.4/0.5 =
16.8
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2 years ago
Sophie Ruth is eating a
Firdavs [7]

Answer:

15 grams

Step-by-step explanation:

There is a 50 gram chocolate bar that contains 30% cocoa. So we are basically finding 30% of 50. We break 30 into 3*10 and 50 into 5*10. 5*3 = 15.

Therefore, there are 15 grams of cocoa in the chocolate bar.

I hope this helps.

6 0
3 years ago
Can someone plzzz help me with this math practice paper
weeeeeb [17]

Answer:

45 degrees for 8

135 degrees for 9

48 for 10

Yes a square is a rectangle

Next ones.

Sut = 21 becuase x=5

7

Step-by-step explanation:

Last one:

x^2 + 8 = 3x + 36

      - 8          -  8

x^2        = 3x + 28

     -3x       -3x

x^2 - 3x =     28

(x · x) - 3x = 28.        

This was were a little guess work was used,

I found that any number lower than 7 is less than 28 when pluged into x and any above is higher.

Hence x = 7

So

x^2 + 8 = 7^2 + 8

7 x 7 = 49.    49 + 8 = 57.

and

3x+36 = 7 x 3 + 36

7x3 = 21. 21 + 36 = 57.

Both lines are equal so x is indeed 7.

The RSTU rectangle

3x+6 = 5x-4

    +4        +4

3x+10 = 5x

-3x        -3x

10 = 2x

10/2 = 5

5 = x or x = 5

plug it in now

3 x 5 = 15. 15 + 6 = 21

and

5 x 5 = 25. 25 - 4 = 21

so x = 5

8-10

QRS = 45 degrees because bisects the square with a diagonal line from corner to corner

PTQ is a 135 degrees because it is wider than a 90 degrees angle and meets both upper corner from the middle of the square making it 135 degrees.

SQ = 48 because RT = 24 and RT is half the length of SQ meaning its length would be 48

Or

SQ= 24 degrees because RT = 24 and if RT was to continue on the line it is on it will reach the length of SQ.

3 0
3 years ago
The graph represents the cost y (in dollars) to open an online gaming account and buy x games. Write an equation in slope-interc
Luba_88 [7]

Answer:

y = 10x + 15

Step-by-step explanation:

you pick two points on the line

I picked (3,45) and (6,75)

you subtract the two x’s and y’s

75 - 45 = 30 (30 is the rise) you go up from 45 to 75

6 - 3 = 3 (you move 3 times to the right to get to the 6) so 3 is the run

slope = rise/run so 30/3 = 10

The y-intercept is the place you start on the graph so that is 15

8 0
3 years ago
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Answer:

a <= 3

Step-by-step explanation:

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