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kondaur [170]
2 years ago
10

If 4sintheta = -3, solve for theta given 0°>_theta>_360°

Mathematics
1 answer:
Soloha48 [4]2 years ago
6 0

Answer:

311.41 degrees

Step-by-step explanation:

If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).

Let's assume we're in Quadrant IV.  Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.

According to the Pythagorean Theorem,  (-3)^2 + x^2 = 4^2, or,

x^2 = 16 - 9 = 7.

Then x is either √7 or -√7.

To find the angle Ф, use the inverse sine function:

Ф = arcsin (-3/4).  Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees.  We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."  

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What is the distance between the points (3, 5) and (3, 1)?
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Answer:

4

Step-by-step explanation:

The x coordinate is the same so the distnce is only the difference in y

5 - 1 = 4

8 0
2 years ago
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Create a factorable polynomial with a GCF of 6. Rewrite that polynomial in two other equivalent forms. Explain how each form was
mel-nik [20]
We are asked in the problem to devise a polynomial equation that has a GCF of 6 which means each of the terms can be divided to 6. For example: 6*(x^2 + x+1) = 6x^2 + 6x +6. This polynomial is created by multiplying each terms by the number 6 which is distinguished by factoring. 
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How do you find your y-intercept from your x-y points?
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5 0
2 years ago
John and Jane are married. The probability that John watches a certain television show is .7. The probability that Jane watches
ikadub [295]

a) The probability  that both John and Jane watch the show is 0.12.

b.The probability that Jane watches the show, given that John does is  0.1714.

c)They do watch show independent of each other.

Step-by-step explanation:

Here, as given in the question:

Probability that John watches a certain show  = 0.7   ⇒ P(J) = 0.7

Probability that Jane watches a certain show  = 0.3   ⇒ P(Je) = 0.3

Probability that John watches a certain show given Jane watches it to

 = 0.4   ⇒ P(J/Je) = 0.4

a. )  Here, we need to find the probability of  both Jane and John watching a show , P(J∩Je)

Now, by BAYES THEOREM:

P(J/Je)  = \frac{P(J \cap Je)}{P(Je)}

\implies  0.4  = \frac{P(J \cap Je)}{0.3} \\\implies P(J \cap Je) = 0.4 \times 0.3  = 0.12

Hence the probability  that both John and Jane watch the show is 0.12.

b.) The probability that Jane watches the show, given that John does is P(J/Je)

By BAYES Theorem:

P(Je/J)  = \frac{P(J \cap Je)}{P(J)}\\\implies P(Je/J)  = \frac{0.12}{0.7}  = 0.1714

Hence, the probability that Jane watches the show, given that John does is  0.1714.

c) As we can see P(Jane ∩ John) =  0.12

So, the probability of both of them seeing the show TOGETHER is 0.12.

Hence, they do watch show independent of each other and the probability of doing that is 1.0.12  = 0.88

7 0
3 years ago
Find the area of a regular nonagon with a side length of 7 and an apothem of 5
vitfil [10]
A NONA=9, nonagon has 9 sides, so it's perimeter is 7+7+7+7+7+7+7+7+7, or 63, and we know the apothem.

bearing in mind that the area of a regular polygon is 
(1/2)ap   a = apothem, p = perimeter

so in this case that'd be (1/2)(5)(63).
7 0
3 years ago
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