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3 years ago

If cos A = 1/3 , then what is the positive value of sin 1/2A, in simplest radical form with a rational denominator?

Mathematics

1 answer:

wolverine [178]3 years ago

5 0

Answer:

Step-by-step explanation:

You should remember from theory (one is the formula of the cosine of the double angle, and the other is the classic sum of squares being 1). $cos A = cos^2 \frac A2 - sin^2 \frac A2 = 1- 2sin^2 \frac A2$

At this point let's grab the first and last step of the chain, replacing values:

$\frac 13 = 1-2sin^2\frac A2 \rightarrow 2sin^2 \frac A2 =\frac23\\sin^2 \frac A2 = \frac13 \rightarrow sin \frac A2 = \frac{1}{\sqrt3} = \frac{\sqrt3}{3}$

Last passage you multiply top and bottom by the square root of 3 to rationalize.

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Answer:

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3 years ago

Round 78482 to the nearest thousand

shtirl [24]

Answer:

78,000

Explanation:

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3 years ago

The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we w

Sati [7]

Answer:

The sample size is $n = 600$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The margin of error is $MOE = 0.04$

Given that the confidence level is 95% the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the values is

$Z_{\frac{\alpha }{2} } = 1.96$

The reason we are obtaining critical value of $\frac{\alpha }{2}$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while