Suppose that cot θ = c and 0 < θ < π 2 . what is a formula for sin θ in terms of c?

2 answers:

8 0

For this case we have the following equation:
cot θ = c
Rewriting we have:
cosine (θ) / sine (θ) = c
From here, we must clear the value of the sinus (θ).
We have then:
sine (θ) = (1 / c) * cosine (θ)
Answer:
a formula for sin θ in terms of c is:
sine (θ) = (1 / c) * cosine (θ)

blsea [12.9K]2 years ago

5 0

Answer:

Sinθ = 1/√c²+1 in terms of c

Step-by-step explanation:

Given cotθ = c and 0 < θ < 2π

Cot θ = 1/tanθ = c

tanθ = 1/c

From SOH, CAH, TOA

tanθ = opposite/adjacent = 1/c

This shows that opposite = 1

adjacent = c

Sinθ = opposite/hypothenuse

Before we can get sinθ, we need the hypotenuse side. Using Pythagoras theorem to get the hypotenuse. According to the theorem, adj²+opp² = hyp²

hyp² = c²+1²

hyp² = c²+1

hyp = √c²+1

Sinθ = 1/√c²+1 in terms of c

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In a production process, the diameter measures of manufactured o-ring gaskets are known to be normally distributed with a mean d

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Answer:

DIRECT WAY EXCEL

"=NORM.DIST(75,80,3,TRUE)"

And we got: $P(X\leq 75)= 0.04779$

OTHER WAY

$P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z$

And we can find this probability using the normal standard table or excel:

$P(Z$

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

$X \sim N(80,3)$

Where $\mu=80$ and $\sigma=3$

And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:

$P(X\leq 75)$