Find the exact value of csc theta if tan theta = sqrt3 and the terminal side of theta is in Quadrant III.

Find The Exact Value Of Csc Theta If Tan Theta = Sqrt3 And The Terminal Side Of Theta Is In Quadrant

Answers

Answer 1

Answer:

3rd option

Step-by-step explanation:

Using the identities

cot x = [tex]\frac{1}{tanx}[/tex]

csc² x = 1 + cot² x

Given

tanθ = [tex]\sqrt{3}[/tex] , then cotθ = [tex]\frac{1}{\sqrt{3} }[/tex]

csc²θ = 1 + ([tex]\frac{1}{\sqrt{3} }[/tex] )² = 1 + [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

cscθ = ± [tex]\sqrt{\frac{4}{3} }[/tex] = ± [tex]\frac{2}{\sqrt{3} }[/tex]

Since θ is in 3rd quadrant, then cscθ < 0

cscθ = - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = - [tex]\frac{2\sqrt{3} }{3}[/tex]


Related Questions

anyone know this ‍♀️ ??

Answers

Answer:

B. 4 cups

Step-by-step explanation:

trust me

Select the equivalent expression.




Umm so yeah... happy pride month royals!

Answers

Answer:

Step-by-step explanation:

The first answer is correct because you are really not changing anything about the question

What point is the intersection of the graphs of the line x−y=12 and x+y=−10 ?

Answers

Answer:

(1, -11)

The correct answer is B

pls help! its due today i would mark u brainliest! but pls it's an emergency do both problems!

Answers

Answer:

Step-by-step explanation:

The coordinate is (x,-y)

Decide if 7x+3=4x+3 has no solution, one solution, or infinitely many solutions

Answers

Answer:

0, one solution

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

7x+3=4x+3 only has one solution which is x = 0.

Hope this helps! :)

Try using symbolab if you're confused

A hot air balloon is 45 meters above the tall seat building in a city write a equation to show the height b of the balloon if the building is t meters tall

Answers

Answer:

b = t + 45

Step-by-step explanation:

Position of hot air Ballon = 45 meters above tall seat building ;

Height of tall seat building = t

Height of Ballon, b = height of tall seat building + 45 m

Hence,

b = t + 45

How many liters of 10% silver iodide mixed with 9 liter of a 4%silver iodide solution to get 6% solution

Answers

Answer:

The correct answer is "4.5 liters". A further explanation is provided below.

Step-by-step explanation:

Let the solution needed be "x".

then, according to the question,

⇒ [tex]4 \ percent(9)+10 \ percent(x)=6 \ percent(9+x)[/tex]

By solving the above expression, we get

⇒ [tex]0.04\times 9+0.1x=0.06\times 9+0,06\times x[/tex]

⇒                [tex]0.04 x=0.54-0.36[/tex]

⇒                [tex]0.04x=0.18[/tex]

⇒                      [tex]x=\frac{0.18}{0.04}[/tex]

⇒                         [tex]=4.5 \ liters[/tex]

In the diagram of
△△NRQ below, SP∥∥RQ, NS=10, SR=50, and PQ=40. What is the length of NQ?

Answers

Answer:

Step-by-step explanation:

A ship is sighted from the top of a lighthouse. The angle of depression from the lighthouse to the ship is 45degrees. The distance from the top of the lighthouse directly to the ship is 4miles.Calculate the horizontal distance of the ship from the bottom of the lighthouse

Answers

Answer:

[tex]2\sqrt{2} \text{ mi}[/tex]

Step-by-step explanation:

See the attached image for a picture of the situation.  The angle of depression lets you find the angle next to it but inside the triangle.  It, too, must measure 45 degrees.

That means the triangle is an isosceles triangle (two legs of equal length).

Apply the Pythagorean Theorem.

[tex]x^2+x^2=4^2\\2x^2=16\\x^2=18\\x=\sqrt{8}=2\sqrt{2}\approx 2.83\text{ mi}[/tex]

Question 6 The mineral content of a particular brand of supplement pills is normally distributed with mean 490 mg and variance of 400. What is the probability that a randomly selected pill contains at least 500 mg of minerals

Answers

Answer:

0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Mean 490 mg and variance of 400.

This means that [tex]\mu = 490, \sigma = \sqrt{400} = 20[/tex]

What is the probability that a randomly selected pill contains at least 500 mg of minerals?

This is 1 subtracted by the p-value of Z when X = 500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 490}{20}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals

The probability is 0.3085.

Let X=the amount of minerals.

We have to find P(X≥500).

Mean = 490.

Standard deviation = [tex]\sqrt{400}=20[/tex].

z score of 500 is = [tex]\frac{500-490}{20 } =0.5[/tex].

So, P(X≥500) = P(z≥0.5) = 1 - P(z<0.5) = 1-0.6915=0.3085.

Learn more: https://brainly.com/question/14109853

People were surveyed about the types of pets they own and their housing situation. Each person has only one pet. For people who live in a condo, what is the relative frequency with which a person owns a cat?

Answers

Answer:

The answer is 6.3

Step-by-step explanation:

The radius of a circle is 2 meters. What is the circle's circumference?
r=2 m
Use 3.14 for pi.
Pls helpp

Answers

Answer:

12.56

Step-by-step explanation:

C=2πR

Circumference equals two times Pi times radius

Does the table show growth or decay?

Answers

Answer:

growth because the numbers are clearly getting higher.

GROWTH

because each x theres more and more y

Which line has a slope of -2 and y-intercept of 3

Answers

Answer:

A

Step-by-step explanation:

The line has to go down when x move to the right due to the negative slope. So B and C cannot be right.

The line has to pass through (0,3), that's the y-intercept, so A and D can still both be right.

For every step to the right, the line has to move 2 down (slope -2). Only A does that. D moves 0.5 down for every step to the right.

A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs Rs 15 per litre, a. Write a numerical expression for the given statement. B. Which property of whole numbers would you use to form a numerical expression for the given statement? C. How much money he gets per day for the supply?

Answers

Answer:

a) (15 × 32) + (15 × 68)

b) Distributive property

c) $1500

Step-by-step explanation:

A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs Rs 15 per litre,

a. Write a numerical expression for the given statement.

The numerical expression for the given statement is written as:

$15 × 32 liters + $15 × 68 liters

15 × 32 + 15 × 68

B. Which property of whole numbers would you use to form a numerical expression for the given statement?

The property that I would use to form a numerical expression is a distributive property

a × (b + c) = (ab + ac)

Where a = $15

b = 32 liters

c = 68 liters

Hence:

15 (32 + 68) = (15 × 32) + (15 × 68)

C. How much money he gets per day for the supply?

The amount he gets per day:

15 (32 + 68) = (15 × 32) + (15 × 68)

= $1500

3(2 + 4) = (3•2)+(3•4) is an
example of which property?

Answers

Answer:

Distributive Property

Step-by-step explanation:

Distributive property

How do you solve (-10) - (-3)

Answers

Answer:

-7

Step-by-step explanation:

-10 - -3

- 10 + 3

-7

(a double negative becomes a positive)

Answer:

-7

Step-by-step explanation:

please help its easy im just not smart enough to do it lma0

Answers

Answer:

20 feet

Step-by-step explanation:

66/3.3

it's twenty i dont know what else to say

Answer:

20m

Step-by-step explanation:

1m = 3.3ft

66 feet = 20m

 


a. y-4=1/4(x-4)
b. y-12=1/4(x-6)
c. y-12=4(x-6)
d. y-6=4(x-12)
e. y-4=4(x-4)
f. y-6=1/4(x-12)

Answers

Answer:

f. y-6 = 1/4(x-12)

Step-by-step explanation:

the slope eliminates some options right away :

slope = y/x = 1/4, because x has to increase by 8 units for y to increase by 2 unit (or then simplified 4 units for 1).

so, we only need to look at equations with 1/4 as factor of x.

a. covers (12,6) but not (4,4) - wrong

b. covers none of the 2 points - wrong

c., d., e. have the wrong slope

f. is right. for x=12 y is then 6. for x=4 y is then also 4. correct !

PLEASE HELP QUICK ITS TIMED



Dawson has 3 more tokens than twice the number of tokens that Rachel has. Dawson has
21 tokens. What is the total number of tokens Rachel has?

Answers

Answer:

9

Step-by-step explanation:

I think what they are asking is to subtract the 3 tokens from 21 tokens he already has giving us 18. and since it says "Twice the number of tokens" I'm assuming you divide 2 from 18 giving you 9 tokens.

Answer:

9 divided by 21

Step-by-step explanation:

17

The figure below is a square inside a rectangle

Answers

Answer:

ummmm their isn't no picture showing

have a good day :)

Step-by-step explanation:

Find the volume of the triangular prism.​

Answers

Answer:

theres no picture

Step-by-step explanation:

PLEASE!!! I JUST REALLY NEED HELP RIGHT NOW! T∆T
Using the 45o -45o -90o triangle theorem, solve this triangle.​

Answers

Answer:

[tex] k = 24 \sqrt{2} [/tex]

Step-by-step explanation:

Given is a 45° - 45° - 90° triangle.

According to the 45° - 45° - 90° triangle theorem, measure of the side opposite to 45° angle is equal to [tex] \frac{1}{\sqrt 2} [/tex] times of the hypotenuse.

[tex]\therefore 24 = \frac{1}{ \sqrt{2} } k \\ \\ \therefore \: 24 \sqrt{2} = k \\ \\ \therefore \:k = 24 \sqrt{2} [/tex]

Answer:

Step-by-step explanation:

take 45 degree as reference angle

using cos rule

cos 45=adjacent/hypotenuse

1/[tex]\sqrt{2}[/tex]=24/k(do cross multiplication)

24*[tex]\sqrt{2}[/tex] =k*1

24[tex]\sqrt{2}[/tex] =k

A cylinder has a diameter of 10cm. The height of the cylinder is 2 5 the length of the diameter. Calculate the volume of the cylinder in terms of π.

Answers

Answer:

625 π cm^3

Step-by-step explanation:

volume of a cylinder = πr^2h

π = 22/7

r = radius = 10/2 = 5cm

the diameter is the straight line that  passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

π x (5^2) x 25 = 625 π

Two dice are rolled
simultaneously.
Find the probability of getting
same number on both the dice.

Answers

Answer:

Here is ur answer!!!! have a nice day ahead...

hey! i’ll give brainliest help thanks

Answers

Answer:

A government by the people

Step-by-step explanation:

The answer is definitely a


Solve the rational equation:
9/x + 1/4 =2/x

Answers

Answer:

D, x=-28

Step-by-step explanation:

Answer:

[tex]x=-28[/tex]

Step-by-step explanation:

[tex]\frac{9}{x} +\frac{1}{4} =\frac{2}{x}\\[/tex]

Move [tex]\frac{9}{x}[/tex] over the equal sign

[tex]\frac{1}{4} =\frac{2}{x} -\frac{9}{x}[/tex]

[tex]\frac{1}{4} =\frac{-7}{x}[/tex]

Cross multiply

[tex]4*-7/x[/tex]

[tex]\frac{-28}{x}[/tex]

[tex]x=-28[/tex]

Hope this is helpful

Without using a calculator, evaluate 3675° - 3680 x 3670 by using special algebraic
identities.​

Answers

Answer:

13,505,599 good luck

Answer:

3675

3680-

0015

3670

15

18350

3670+

1202

Helpppp please!!!!!!

Answers

Im guessing it’s b if I’m wrong plz don’t mad

As head of the Parks Department, Jada has been tracking the park’s use of different supplies over the last several years. Her research shows that, up through last year, the park’s total water usage per year was 13,505 gallons for all regular days, plus another 18.5 gallons for each special event hosted by the park. How many special events did the park host last year? Show your work.

Answers

Answer:6 events

Step-by-step explanation:

13505+ 18.5x =13616

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