All categories

1 year ago

Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

1 answer:

5 0

$\sin^{2} \theta+\cos^{2} \theta=1 \\ \\ \sin^{2} \theta+\left(\frac{\sqrt{3}}{3} \right)^{2}=1 \\ \\ \sin^{2} \theta+\frac{1}{3}=1 \\ \\ \sin^{2} \theta=\frac{2}{3} \\ \\ \theta=-\frac{\sqrt{2}}{\sqrt{3}}=\boxed{-\frac{\sqrt{6}}{3}}$

You might be interested in

URGENT PLEASE HURRY I'M RUNNING OUT OF TIME!!!!!

tester [92]

2.15
1hr is 60 min so
60÷15=4
45miles×2hrs=90
45÷4=11.25
90+11.25=101.25 miles
101.25 miles÷ 25 miles per gallon= 4.05 gallons
4.05 gallons× $2.75 per gallon= $11.1375
$11.1375= $11.14
Alicia spends $11.14 on gas to get to work

7 0

3 years ago

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person se

notsponge [240]

Answer:

2.28% probability that a person selected at random will have an IQ of 110 or higher

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 100, \sigma = 5$

What is the probability that a person selected at random will have an IQ of 110 or higher?

This is 1 subtracted by the pvalue of Z when X = 110. So

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

$Z = \frac{110 - 100}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.0228

2.28% probability that a person selected at random will have an IQ of 110 or higher

5 0

3 years ago

6 2/3−4 4/9=?<br><br> six and two over three minus four and four over nine equals?

In-s [12.5K]

The answer is 2 2/9.

8 0

3 years ago

Read 2 more answers

Melissa puts 2/5 of her babysitting money in savings and uses 1/2 of the remaining money to go to the movies. If she has $12 lef

ser-zykov [4K]

If you work backwards, she had 24 before going to the movies. This is 3/5 of what she had originally. Use this to find 1/5 the but dividing 24 by 4 = 8 then multiply by 5 to get back to the original value 8 x 5 = 40

8 0

2 years ago

Read 2 more answers

Here are two steps from the derivation of the quadratic formula.

Lana71 [14]

What took place between the first step and the second step? - A. Taking the square root of both sides.

As we can see from the first to second step, the left side of the equation goes from being squared to not being squared. While on the right side of the equation, the square root is now being taken.

Hope this helps!! :)

6 0

3 years ago

Read 2 more answers