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Marina86 [1]
2 years ago
11

For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?

Mathematics
1 answer:
rosijanka [135]2 years ago
7 0

Answer:

  • sinθ = 3/5
  • cosθ = 4/5

<h3>Given </h3>
  • Point (16, 12)

<h3>To find </h3>
  • Sine and cosine of the angle, using the given coordinates

<h3>Solution</h3>

Since both of the coordinates are positive, we have:

  • the angle θ is in the first quadrant, both sine and cosine have positive values;
  • the x-coordinate determines the value of adjacent leg;
  • the y-coordinate determines the value of opposite leg.

Find the hypotenuse of the right triangle using values of both legs:

  • h=\sqrt{ x^2+y^2}=\sqrt{16^2+12^2}= \sqrt{400} =20

Find sine:

  • <em>sine = opposite/hypotenuse</em>
  • sinθ = 12/20 = 3/5

Find cosine:

  • <em>cosine = adjacent/hypotenuse</em>
  • cosθ = 16/20 = 4/5

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4 0
2 years ago
In the parallelogram DEFG, DH=x+1, HF=3y, GH=3x-4, and HE=5y+1. Find the values of x and y. The diagram is not drawn to scale.
RideAnS [48]

Answer:

Step-by-step explanation:

Given:  In parallelogram DEFG,

DH = x + 1

HF = 3y

GH = 3x - 4

and HE = 5y + 1

Solution: Since, DH,HF, GH and HE represents the diagonals of the parallelogram and we know that the diagonals of the parallelogram bisect each other, therefore

x+1=3y            (1)

3x-4=5y+1      (2)

Multiply equation (1) with 3 and then subtract equation (2) from it, we get

3x+3-3x+4=9y-5y-1

7=4y-1

y=2

Substituting the value of y=2 in equation (1), we get

x+1=3(2)

x=5

Therefore, the value of x and y are 5 and 2 respectively.

8 0
3 years ago
Hans deposits $300 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the
blagie [28]
300 x 0.02 x 5 = 30
answer
<span> interest will $30 in the first 5 years</span>
5 0
3 years ago
What is the answer to this
astraxan [27]
It is convenient to do part b first, then use that result to do part a.

b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end.
Adding (a, b) to the above equation gives
  2(a, b) - (x1, y1) = (x2, y2)
Adding (x1, y1) then gives
  2(a, b) = (x1, y1) + (x2, y2)
Finally, dividing by 2 gives a formula for (a, b):

  (a, b) = ((x1, y1) + (x2, y2))/2
The midpoint is the average of the end points.

a. Using the result from part b, the midpoint is
  midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2
  midpoint = (4, 5)
5 0
3 years ago
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