All categories

3 years ago

Given sin x=0.3 , what is cos x ?

Mathematics

2 answers:

blsea [12.9K]3 years ago

7 0

Cos x = sqrt( 100 - 9) / 10
= 0.9539392014sin x = 0.3 = 3/10

shusha [124]3 years ago

7 0

Answer: The value of $\cos x$ is 0.95.

Step-by-step explanation: Given that, for an angle x,

$\sin x=0.3.$

We are given to find the value of $\cos x.$

We will be using the following trigonometric identity:

$\cos^2x+\sin^2x=1.$

We have

$\cos^2x+\sin^2x=1\\\\\Rightarrow \cos^2x=1-\sin^2x\\\\\Rightarrow \cos x=\sqrt{1-\sin^2x}\\\\\Rightarrow \cos x=\sqrt{1-(0.3)^2}\\\\\Rightarrow \cos x=\sqrt{1-0.09}\\\\\Rightarrow \cos x=\sqrt{0.91}\\\\\Rightarrow \cos x=0.95.$

Thus, the value of $\cos x$ is 0.95.

You might be interested in

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

Fraction 5\6 x 3\10 what is the answer?

Katarina [22]

15/60 *Simplified Answer: 1/4

5 0

3 years ago

The ratio of girls to boys in Mr. Smith's homeroom is 3:4. The ratio in Mr. Smith's homeroom to students in the whole 7th grade

Leno4ka [110]

3:4 = G:B

1:5 = Mr. Smith's class: 7th Grade

2:7= 7th: Middle school

12 girls = 3 units

1 unit = 12/3= 4

Boys = 4x4= 16

Whole class = 28 students

Class : Grade = 1:5 7 = number of units in Mr. Smith's class

28 = 1 unit

5 units= 28x5= 140 There are 140 kids in the grade

140 = 2 units

1 unit = 140/2= 70

70x7=490

There are 490 students in the whole grade

6 0

3 years ago

At the beginning of each year for 14 years, Sherry Kardell invested $400 that earns 10% annually. What is the future value of Sh

Naddik [55]

Hmm if I'm not mistaken, is just an "ordinary" annuity, thus

$\bf \qquad \qquad \textit{Future Value of an ordinary annuity}
\\\\
A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]
\\\\\\$

$\bf \begin{cases}
A=
\begin{array}{llll}
\textit{original amount}\\
\textit{already compounded}
\end{array} &
\begin{array}{llll}

\end{array}\\
pymnt=\textit{periodic payments}\to &400\\
r=rate\to 10\%\to \frac{10}{100}\to &0.1\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, so once}
\end{array}\to &1\\

t=years\to &14
\end{cases}
\\\\\\
A=400\left[ \cfrac{\left( 1+\frac{0.1}{1} \right)^{1\cdot 14}-1}{\frac{0.1}{1}} \right]
$

3 0

3 years ago

Read 2 more answers

The ecology club wants to collect 200 bags of trash for a cleanup.Before lunch they collected 87 bags.After lunch they collected

Naddika [18.5K]

Answer:

18 more bags

Step-by-step explanation:

87 + 95 = 182

200 - 182 = 18

8 0

3 years ago