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1 year ago

15

Find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.)

3π 4

2 answers:

Julli [10]1 year ago

5 0

Angle x = 3 π / 4 = 135°
The angle is in the 2nd Quadrant.
Answer:
sin x = √2 / 2
cos x = - √2/ 2
tan x = - 1
cot x = - 1.

Vladimir79 [104]1 year ago

3 0

Trigonometric ratios value for the angle

$sin\frac{\pi }{4}=\frac{1}{2} \sqrt{2}$

$cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}$

$tan\frac{\pi }{4}=-1$

$cot\frac{\pi }{4}=-1}$

$sec\frac{\pi }{4}=-\sqrt{2}$

$csc\frac{\pi }{4}=\sqrt{2}$

<h3>Further explanation</h3>

The angle of a triangle expressed in trigonometric ratios

The angle can change from 0° to 360°

In the Cartesian field, there are 4 regions called quadrants.

1. quadrant 1: 0 <a <90
2. quadrant 2: 90 <a <180
3. quadrant 3: 180 <a <270
4. quadrant 4: 279 <a <360

In this quadrant, the positive angle is (meaning another angle will be negative value)

1. quadrant 1: all angles
2. quadrant 2: sin and csc
3. quadrant 3: tan and cot
4. quadrant 4: cos and sec

The angle x with an angle of 3/4π

$\frac{3}{4}\pi=(\pi-\frac{1}{4}\pi)=\frac{\pi }{4}$

The angle x is in quadrant 2, so the angle that is positive value is only sin and csc

Then the exact trigonometric ratios value for the angle

$sin\frac{\pi }{4}=\frac{1}{2} \sqrt{2}$

$cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}$

$tan\frac{\pi }{4}=-1$

$cot\frac{\pi }{4}=-1}$

$sec\frac{\pi }{4}=-\sqrt{2}$

$csc\frac{\pi }{4}=\sqrt{2}$

<h3>Learn more</h3>

trigonometric identities

brainly.com/question/5013374#

trigonometric ratio to find x

brainly.com/question/9880052

trigonometric ratios for triangle XYZ

brainly.com/question/10782297

Keywords: quadrant, trigonometry, angle, ratios

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Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

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

$df=n-1=8-1=7$

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

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

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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1 year ago

Find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the top side is parallel to the

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Answer:

Here is the continuation to the question ; The buoyant force is the difference between the fluid forces on the top and bottom of the solid. (The weight-density of water is 62.4 pounds per cubic foot.)

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Step-by-step explanation:

The steps are as shown in the attachment.

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Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of

nikitadnepr [17]

Answer:

a) Reject H₀

b) [0.31; 3.35]

Step-by-step explanation:

Hello!

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The study variable is:

Y: Production rate of an assembly line.

Assuming that the study variable has a normal distribution for each population, the observations are independent and the population variances are equal, you can apply a parametric ANOVA with the hypothesis:

H₀ μ₁= μ₂= μ₃

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Where:

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Population 2: line B

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This test is always one-tailed to the right. The statistic is the Snedecor's F, constructed as the MSTr divided by the MSEr if the value of the statistic is big, this means that there is a greater variance due to the treatments than to the error, this means that the population means are different. If the value of F is small, it means that the differences between populations are not significant ( may differ due to error and not treatment).

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The p-value is less than the significance level, the decision is to reject the null hypothesis.

At a level of 5%, there is significant evidence to say that at least one of the population means of the production ratio of the assembly lines A, B and C is different than the others.

b) In this item, you have to stop paying attention to the production ratio of the assembly line A to compare the population means of the production ratio of lines B and C.

(I'll use the same subscripts to be congruent with part a.)

The parameter to estimate is μ₂ - μ₃

The populations are the same as before, so you can still assume that the study variables have a normal distribution and their population variances are unknown but equal. The statistic to use under these conditions, since the sample sizes are 6 for both assembly lines, is a pooled-t for two independent variables with unknown but equal population variances.

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Sa√(1/n₂+1/n₃)

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I hope it helps!

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1 year ago

(1 point) Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the

Vanyuwa [196]

Answer:

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Step-by-step explanation:

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19000x = 304000

x = 304000 / 19000

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In 16 years the populations of the suburb and the city be equal

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