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2 years ago

Can someone make my day and please help me solve number 3?

Mathematics

1 answer:

olga nikolaevna [1]2 years ago

6 0

X = cost of car before tax

Total cost = (cost of car before tax) + (tax amount)
Total cost = x + 5% of x
Total cost = x + 0.05x
Total cost = 1.05x

The total cost is given to be $14,512, which means

<span>Total cost = 1.05x = 14512
</span>
1.05x = 14512
1.05x/1.05 = 14512/1.05
x = 13,820.95238
x = 13,820.95

The total cost of the car before tax, to the nearest cent, is $13,820.95

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And for this case since we ar einterested on $-\frac{\pi}{3}$ and we know that the if we are below the y axis the sine would be negative then:

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We can use the notabl angle $\pi/4$ and we know that :

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Then we know that $5\pi/4$ correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

Step-by-step explanation:

For this case we can use the notable angls given on the picture attached.

Part a

For this case we can use the fact that $sin (\pi/3) = \frac{\sqrt{3}}{2}$

And for this case since we ar einterested on $-\frac{\pi}{3}$ and we know that the if we are below the y axis the sine would be negative then:

$sin (-\pi/3) = -\frac{\sqrt{3}}{2}$

Part b

From definition we can use the fact that $tan x= \frac{sin x}{cos x}$ and we got this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}$

We can use the notabl angle $\pi/4$ and we know that :

$sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}$

Then we know that $5\pi/4$ correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

$tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$

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