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Inga [223]
3 years ago
8

Verify the identity. cot(x - pi/2) = -tan(x)

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
8 0

Answer:

See below.

Step-by-step explanation:

\cot(x-\frac{\pi}{2})=-\tan(x)

Convert the cotangent to cosine over sine:

\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)

Use the cofunction identities. The cofunction identities are:

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

To convert this, factor out a negative one from the cosine and sine.

\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)

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Find the values of x and y ???? <br><br> show step plz​
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Answer:

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Step-by-step explanation:

Since the two sides of this triangle are equal in lengths, you know that it is an isosceles triangle.

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6 0
2 years ago
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Which expression is equivalent to 6^-3
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3 years ago
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Scores turned in by an amateur golfer at a golf course during 2017 and 2018 are as follows.
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Answer:

For 2017 Season:

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For 2018 Season:

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Step-by-step explanation:

The following formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where;

n = number of values = 8

x = each value

For 2017 Season

Mean = (73 + 77 + 78 + 76 + 74 + 72 + 74 + 76) / 8 = 600 / 8 = 75

Variance = ((73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 + (74-75)^2 + (76-75)^2) / (8-1) = 30 / 7 = 4.29

Standard deviation = Variance^0.50 = 4.29^0.5 = 2.07

For 2018 Season

Mean = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78) / 8 = 75

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Standard deviation = Variance^0.50 = 27.71^0.5 = 5.26

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3 years ago
The area of a square can be found using the equation A = s², where A is the area and s is the measure of one side of the square.
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