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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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Answer:

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We can use the following excel code: "=1-NORM.DIST(0.1314,0,1,TRUE)"  or the standard normal table

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P(Z>0.01) = 1-P(Z

We can use the following excel code: "=1-NORM.DIST(0.01,0,1,TRUE)"  or the standard normal table

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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Solution to the problem

P(Z>0.1314) = 1-P(Z

We can use the following excel code: "=1-NORM.DIST(0.1314,0,1,TRUE)"  or the standard normal table

P(Z

We can use the following excel code: "=NORM.DIST(0.75,0,1,TRUE)"  or the standard normal table.

P(Z>0.01) = 1-P(Z

We can use the following excel code: "=1-NORM.DIST(0.01,0,1,TRUE)"  or the standard normal table

6 0
3 years ago
Triangle ABC is similar to triangle DEF. The length of AC is 10cm. The length of BC is 16 cm. The length of DF is 8cm. What is t
Zolol [24]

Answer: The length of EF=15 cm.

Step-by-step explanation:

8 0
3 years ago
The circle given by x^2+y^2-6y-12=0 can be written in standard form like this: x^2+(y-k)^2=21 What is the value of k in this equ
sweet [91]

Answer:

The value of k =3

Step-by-step explanation:

x^2+y^2-6y-12=0 We need to solve this equation to become in standard form to find the value of k.

x^2+y^2-6y-12=0\\x^2+y^2-6y = 12\\(x)^2 +(y^2-2(y)(3)+(3)^2) = 12 +(3)^2\\(x)^2+(y-3)^2 = 12+9\\(x)^2 +(y-3)^2 = 21

The given standard form is:

x^2+(y-k)^2=21

Comparing it with (x)^2 +(y-3)^2 = 21

The value of k =3

3 0
2 years ago
Read 2 more answers
Please help me in this question
charle [14.2K]
Number defective=4
number of non-defective=total-defective
=20-4
=16
the questions asked for 1 defective
so we choose only 1 defective from 4 defective items
4C1

and for 1 non-defective
we choose only 1 non-defective from 16 non-defective items
16C1

we choose 2 items from 20 items
so 20C2

answer:
probability= [(4C1) * (16C1)] /(20C2)
=32/95

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What is 30 tens in standard form?
lana [24]
The answer to that would be 300. Hope this helps you out!
8 0
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