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lys-0071 [83]
3 years ago
11

Why is cos (pi/2-theta)=sin theta

Mathematics
1 answer:
sweet [91]3 years ago
4 0

Answer:

Step-by-step explanation:

Hi there,

Please recall the trigonometric identities:

sin\theta=\frac{O}{H}

cos\theta=\frac{A}{H}

In a right triangle, there are three possible angles, one of them being 90 degrees, or π/2 radians. One of them we will designate as θ and the other φ. Since sinθ is the side opposite of it divided by hypotenuse, the cosφ is actually the same ratio! This is because although cosφ is from the other angle's perspective, what it calls "adjacent" is the opposite from perspective of θ. The same will apply if we are talking about sinφ and cosθ Draw a triangle and you will notice this using perspectives.

Since we know for a fact that it must add to π radians inside a triangle, and we already know one of them is always π/2 radians (definition of right triangle), we can do the following:

\pi =\frac{\pi}{2} + \theta + \phi\\\frac{\pi}{2}= \theta + \phi

With this in mind, we have an identity for both θ and φ in terms of the other:

\theta = \frac{\pi }{2} - \phi    \phi = \frac{\pi }{2} - \theta

Now, based on the previous logic:

sin\theta = cos\phi = sin(\frac{\pi}{2} -\phi)=cos(\frac{\pi}{2}-\theta)

Two interesting formulas arise:

sin\theta=cos(\frac{\pi }{2}-\theta) \\ cos\phi= sin(\frac{\pi}{2} -\phi)

Study well and persevere.

If you liked this situation, hit a Thanks or give a Rating!

thanks,

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308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

<h3><u>Combination</u></h3>

Since a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:

  • 385 x 0.06 = 23.1
  • 300 x 0.07 + 85 x 0.02 = 22.7
  • 310 x 0.07 + 75 x 0.02 = 23.2
  • 308 x 0.07 + 77 x 0.02 = 23.1

Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

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4 0
1 year ago
Question Help Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 5656 hours and a
koban [17]

Answer:

a)3.438% of the light bulbs will last more than 6262 hours.

b)11.31% of the light bulbs will last 5252 hours or less.

c) 23.655% of the light bulbs are going to last between 5858 and 6262 hours.

d) 0.12% of the light bulbs will last 4646 hours or less.

Step-by-step explanation:

Normally distributed problems can be solved by the z-score formula:

On a normaly distributed set with mean \mu and standard deviation \sigma, the z-score of a value X is given by:

Z = \frac{X - \mu}{\sigma}

After we find the value of Z, we look into the z-score table and find the equivalent p-value of this score. This is the probability that a score will be LOWER than the value of X.

In this problem, we have that:

The lifetimes of light bulbs are approximately normally​ distributed, with a mean of 5656 hours and a standard deviation of 333.3 hours.

So \mu = 5656, \sigma = 333.3

(a) What proportion of light bulbs will last more than 6262 ​hours?

The pvalue of the z-score of X = 6262 is the proportion of light bulbs that will last less than 6262. Subtracting 100% by this value, we find the proportion of light bulbs that will last more than 6262 hours.

Z = \frac{X - \mu}{\sigma}

Z = \frac{6262 - 5656}{333.3}

Z = 1.82

Z = 1.81 has a pvalue of .96562. This means that 96.562% of the light bulbs are going to last less than 6262 hours. So

P = 100% - 96.562% = 3.438% of the light bulbs will last more than 6262 hours.

​(b) What proportion of light bulbs will last 5252 hours or​ less?

This is the pvalue of the zscore of X = 5252

Z = \frac{X - \mu}{\sigma}

Z = \frac{5252- 5656}{333.3}

Z = -1.21

Z = -1.21 has a pvalue of .1131. This means that 11.31% of the light bulbs will last 5252 hours or less.

(c) What proportion of light bulbs will last between 5858 and 6262 ​hours?

This is the pvalue of the zscore of X = 6262 subtracted by the pvalue of the zscore X = 5858

For X = 6262, we have that Z = 1.81 with a pvalue of .96562.

For X = 5858

Z = \frac{X - \mu}{\sigma}

Z = \frac{5858- 5656}{333.3}

Z = 0.61

Z = 0.61 has a pvalue of .72907.

So, the proportion of light bulbs that will last between 5858 and 6262 hours is

P = .96562 - .72907 = .23655

23.655% of the light bulbs are going to last between 5858 and 6262 hours.

​(d) What is the probability that a randomly selected light bulb lasts less than 4646 ​hours?

This is the pvalue of the zscore of X = 4646

Z = \frac{X - \mu}{\sigma}

Z = \frac{4646- 5656}{333.3}

Z = -3.03

Z = -3.03 has a pvalue of .0012. This means that 0.12% of the light bulbs will last 4646 hours or less.

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Answer:Michelle

And 50

Step-by-step explanation:

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A bag contains colored tiles.
KiRa [710]

Answer:

0.5

Step-by-step explanation:

Add everything together 33+66+33 = 132

Then 66/132, = 1/2 or 0.5

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Find the least number which should be added to 6790 to make it a perfect square​
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Answer:

add 99 to 6790

Step-by-step explanation:

6790 +99 = 6889 which is 83 squared

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