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3 years ago

Find an angle where sine and cosine are equal. find the tangent of that angle

Mathematics

1 answer:

algol133 years ago

6 0

Answer: The angle is $45\°$ and the tangent is 1

Step-by-step explanation:

The angle $\theta$ at wich the functions sine and cosine are equal is $45\°$ . Let's prove it:

$sin (45\°)=0.7071$

$cos (45\°)=0.7071$

Hence:

$sin (45\°)=cos (45\°)$

On the other hand, the tangent function is defined as:

$tan \theta=\frac{sin \theta}{cos \theta}$

Then:

$tan (45\°)=\frac{sin (45\°)}{cos (45\°)}$

$tan (45\°)=\frac{0.7071}{0.7071}$

$tan (45\°)=1$

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According to a polling organization, 24% of adults in a large region consider themselves to be liberal. A survey asked 200 resp

Varvara68 [4.7K]

Answer:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=75 represent the number of people Liberal

$\hat p=\frac{75}{200}=0.375$ estimated proportion of people liberal

$p_o=0.24$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of adults liberal is higher than 0.24:

Null hypothesis: $p \leq 0.24$

Alternative hypothesis: $p > 0.24$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47$

Now we can calculate the p value based on the alternative hypothesis with this probability:

$p_v =P(z>4.47)=0.00000391$

The p value is very low compared to the significance level of $\alpha=0.05$ then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

6 0

3 years ago

HELP PLEASE HELP!!!!!

bagirrra123 [75]

(i): A triangle where all three sides are equal and the same.

(ii): A triangle where all three sides are unequal in length.

(iii): A triangle that has two sides of equal length.

(iv): A triangle where all three internal angles are acute(they measure less than 90 degrees.

(v): A triangle where all three internal angles are obtuse(measure above 90 degrees).

(vi): A triangle where one internal angle is a right angle(90 degrees).

Hope this helps

3 0