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3 years ago

If sin tetha=root3/2, what is cos tetha?

Mathematics

1 answer:

Minchanka [31]3 years ago

6 0

Answer:

The value of cos Ф is ± $\frac{1}{2}$

Step-by-step explanation:

There are important rules for sin Ф and cos Ф

sin²Ф + cos²Ф = 1

sin²Ф = 1 - cos²Ф

cos²Ф = 1 - sin²Ф

∵ sin Ф = $\frac{\sqrt{3}}{2}$

∴ sin²Ф = $(\frac{\sqrt{3}}{2})^{2}$

∴ sin²Ф = $\frac{3}{4}$

→ By using the third rule above

∵ cos²Ф = 1 - sin²Ф

∴ cos²Ф = 1 - $\frac{3}{4}$

∴ cos²Ф = $\frac{1}{4}$

→ Take square root for both sides

∴ cos Ф = ± $\frac{1}{2}$

∴ The value of cos Ф is ± $\frac{1}{2}$

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Basically, you are looking for the ARC SINE of .994 which is
83.72 Degrees
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2 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated $s=86.776$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

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2 years ago

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3 years ago

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Answer:

Step-by-step explanation:

To compare 3,176 and 3,472 using the number line, remember how numbers appear on a number line:

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3 years ago

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FINAL ANSWER: 3 jewelry sets

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3 years ago

If sin tetha=root3/2, what is cos tetha?​

If sin tetha=root3/2, what is cos tetha?