Ask question

Ask question

All categories

2 years 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]2 years 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]2 years 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

You might be interested in

What is the mean of 210 160 200

Allushta [10]

190
You add everything together
Then, divide by however many numbers you have
210+160+200
570 / 3
190
Hope this helps..
Mark Brainliest Please!

6 0

2 years ago

Estimate the indicated probability by using normal distribution as an approximation to the binomial distribution. Estimate P(6)

lianna [129]

Answer:

P(6) = 0.6217

Step-by-step explanation:

To find P(6), which is the probability of getting a 6 or less, we will need to first calculate two things: the mean of the sample (also known as the "expected value") and the standard deviation of the sample.

Mean = np

Here, "n" is the sample size and "p" is the probability of the outcome of interest, which could be getting a heads when a tossing a coin, for instanc

So, Mean = n × p = (18) ×(0.30) = 5.4

Next we we will find the standard deviation:

Standard Deviation = $\sqrt{npq}$

n = 18 and p = 0.3 "q" is simply the probability of the other possible outcome (maybe getting a tails when flipping a coin), so q = 1 - p

Standard Deviation = $\sqrt{npq} = \sqrt{(18)(0.3)(0.7)}$

= 1.944

Now calculate the Z score for 6 successes.

Z = ( of successes we're interested in - Mean) ÷ (Standard Deviation)

=(6-5.4) ÷ (1.944) = 0.309

we have our Z-score, we look on the normal distribution and find the area of the curve to the left of a Z value of 0.309. This is basically adding up all of the possibilities for getting less than or equal to 6 successes. So, we get 0.6217.

5 0

2 years ago

He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports t

kiruha [24]

This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).

Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:

sin θ = opposite side / hypotenuse

sin 45 = 68 miles per hr / flight

flight = 68 miles per hr / sin 45

<span>flight = 96.17 miles per hr</span>

6 0

2 years ago

Boy Scout Troop 2 went backpacking in the Sierras. The scouts hiked 5 1/2 hours each day for 4 days. If their average speed was

KIM [24]

Given :

Time they traveled in a day , $t=5\dfrac{1}{2}=\dfrac{11}{2}\ hours$ .

Average speed , $s=1\dfrac{3}{4}=\dfrac{7}{4}\ mph$ .

To Find :

How far did they hike altogether in 4 days .

Solution :

We know , distance covered is given by :

$d=s\times t \\\\d=\dfrac{7}{4} \times \dfrac{11}{2}\ miles\\\\d=\dfrac{77}{8}\ miles$

So , distance covered in 4 days is :

$D=\dfrac{77}{8}\times 4\ miles\\\\D=38.5\ miles$

Therefore , distance they hike in 4 days is 38.5 miles .

Hence , this is the required solution .

7 0

2 years ago

Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers wh

kumpel [21]

Answer:

$z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123$

The p value for a left tailed test would be:

$p_v =P(z$

Since the p value is very higher we can conclude that the true proportion of teenagers who floss twice a day is NOT less than 40%.

Step-by-step explanation:

Information given

n=400 represent the random sample given

X=149 represent the floss twice a day

$\hat p=\frac{149}{400}=0.3725$ estimated proportion of floss twice a day

$p_o=0.4$ is the value the proportion that we want to check

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to check proportion of teenagers who floss twice a day is less than 40%, so then the system of hypothesis are.:

Null hypothesis: $p \geq 0.4$

Alternative hypothesis: $p < 0.4$

For the one sample proportion test the statistic is given by:

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

If we replace the info given we got:

$z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123$

The p value for a left tailed test would be:

$p_v =P(z$

Since the p value is very higher we can conclude that the true proportion of teenagers who floss twice a day is NOT less than 40%.

6 0

2 years ago