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Troyanec [42]
3 years ago
8

What is the sine value of 7 pi over 6? negative square root 3 over 2 square root 3 over 2 negative 1 over 2 1 over 2?

Mathematics
2 answers:
djverab [1.8K]3 years ago
6 0
First thing to do is to change the radians to degrees so it's easier to determine our angle and where it lies in the coordinate plane.  \frac{7 \pi }{6} * \frac{180}{ \pi }=210.  If we sweep out a 210 degree angle, we end up in the third quadrant, with a 30 degree angle.  In this quadrant, x and y are both negative, but the hypotenuse, no matter where it is, will never ever be negative.  So the side across from the 30 degree reference angle is -1, and the hypotenuse is 2, so the sine of this angle, opposite over hypotenuse, is -1/2
Mashcka [7]3 years ago
4 0

Answer:

-1/2.

Step-by-step explanation:

Let's decompose \frac{7\pi}{6}:

\frac{7\pi}{6}=\pi+\frac{\pi}{6}

So,

sin(\frac{7\pi}{6})=sin(\pi+\frac{\pi}{6})

=sin(\pi)cos(\frac{\pi}{6})+sin(\frac{\pi}{6})cos(\pi)

=\frac{1}{2}(-1)=\frac{-1}{2}.

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Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give t
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Answer:

a) Hence the probability that the average test score in the class of size 25 exceeds 80.

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b) Hence the probability that the average test score for the class of size 64

P ( X > 74) = 0.9838

P ( Z > 2.14) = 0.0003

c) Probability of the difference exceeding 2.2 = 0.9936

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Step-by-step explanation:

Let's assume a normal distribution.

Now,

a) For a class of 25

P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(25) )\\\\= P (Z < 6 / 2.8)\\\\= P ( Z < 2.14)\\= 0.9838\\

P ( Z > 2.14) = 1- 0.9838\\= 0.0162

b)

Similarly:

For the class of 64

P ( X > 74) = P (Z > 80 - 74/ 14\sqrt(64) )\\\\= P (Z < 6 / 1.75)= P ( Z < 3.428)\\= 0.9838\\

P ( Z > 2.14) = 1- 0.9997\\= 0.0003

c) Probability of the difference exceeding 2.2

= P (Z > 2.2/\sqrt{14 * {(1/25) + (1/64}\\

= P (Z > 2.49)\\= 0.9936

P (Z < 2.49)

= 1 - 0.9936

= 0.0064

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Answer:

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Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

If you are asking to convert from Vertex Form to Standard Form, here is how you do this:

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I am joyous to assist you anytime.

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Answer:

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