)Suppose is a real number with 0 < < 4 . Set = sin( − ), = cos( + ), = sin( − ), and = cos(2 − ). Arrange the values , , , and in increasing order, and explain how you determined their order.

Answer:

b < c < a < d

Step-by-step explanation:

P.S - The exact question is -

Given - Suppose x is a real number with 0 < x < [tex]\frac{\pi }{4}[/tex] . Set a = sin([tex]\pi[/tex] - x) ,                                    

             b = cos([tex]\pi[/tex] + x) , c = sin( x - [tex]\pi[/tex]) , d = cos(2[tex]\pi[/tex] - x)

To find - Arrange the values of a, b, c, d in increasing order , and explain

              how you determined their order.

Proof -

Firstly draw a unit circle where you indicate the following

A = ( cos(x), sin(x) )

B = ( cos( [tex]\pi[/tex] - x) , sin ([tex]\pi[/tex] - x) )

C = ( cos([tex]\pi[/tex] + x), sin ([tex]\pi[/tex] + x) )

D = ( cos (2[tex]\pi[/tex] - x) , sin (2[tex]\pi[/tex] - x) )

As we have given that 0 < x < [tex]\frac{\pi }{4}[/tex]

⇒sin (x) and cos(x) are positive and sin(x) < cos(x)

The figure is as follows :

Now

By seeing point B , we can say that

sin ([tex]\pi[/tex] - x) = sin (x) = a

By seeing point C , we can say that

cos([tex]\pi[/tex] + x) = -cos (x) = b

By seeing point C , we can say that

sin( x - [tex]\pi[/tex]) = -sin(x) = c

By seeing point D , we can say that

cos(2[tex]\pi[/tex] - x) = cos(x) = d

As sin(x) < cos(x) ⇒ a < d

   -sin(x) > -cos(x) ⇒ c > b ⇒ b< c

and as we know that -sin(x) < sin(x) ⇒ c < a

∴ we get

b < c < a < d

Does the table or graph represent a linear or nonlinear function?
Explain.

PLS ANSWER WILL GOVE BRAINLEST!

An urn contains three red marbles and four blue marbles. One marble is selected at random, its color is noted, and it is returned to the urn.
Another marble is then selected. What is the probability that the second marble drawn is red?
A.1/2
b:1/7
c:2/7
d:3/7

A company that manufactures memory chips for digital cameras used the formula c= 126\root(3)(n^(2))+ 1257 to determine the cost c, in dollars, of producing n chips. How much will it cost to produce 230 chips?

Max and Tyler collected 174 plastic bottles from the playground. Tyler collected twice as
many plastic bottles as Max.
Enter the number of plastic bottles that Tyler collected.

Graph the solution of this inequality

Plz help!!! 10 pts..

Round 543,539 to the nearest hundred thousand

Which set of data has the strongest linear association?

SuRpRiSE shAwTYYyyyyyyyyyyyyyyyy​

The sail of a boat is in the shape of a right triangle, as shown below:

The sail of a boat is a right triangle with an acute angle equal to 40 degrees and the side adjacent to the 40 degrees angle is

Which expression shows the height, in meters, of the sail? (6 points)

Select one:
a. 2 divided by sec 40 degrees
b. 2 cosec 40°
c. 2 sin 40°
d. 2 divided by cot 40 degrees

x=4y+1
in slope intercept form

13.) The leading scorer in your high school's hockey league finished the season with an average of 4 goals per game for 15 games. As the leagues
second leading scorer, you have an average of 4 goals per game for 14 games. You still have to play your last game. How many goals must you
score in the final game to overtake the leagues' leading scorer?

150 miles to 4 hours ratio

​Together, teammates Pedro and Ricky got 2675 base hits last season. Pedro had 279 more hits than Ricky. How many hits did each player​ have?

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool

What was the original height of the water in the pool in fet

CAN YOU PLS HELP ME I BEG YOU I WILL GIVE YOU BRAINLET ND SIXTY POINTS pllls i beg you
math!!!

Find the square root of 64a^2/9b^2+4+32a/3b​

Could someone help with 15x-10 factorised

Danielle and Michelle visited a candy shop. Danielle bought 10 pounds of strawberry taffy and 1 pound of banana taffy for $46. Michelle bough 1 pound of strawberry taffy and 1 pound of banana taffy for $10. How much does each type of taffy cost?

Will give Brainliest!!!
What is the y=mx+b of the equation 5x−2y=16

Cook´s bakery is making 15 cakes . Each contains 2 cups of flour . How many cups of flour {f} are needed to make all the cakes

Write the equation of the line given a slope of 0 through the point (5, -7)

✨✨ Easy points for anyone who is good at finding slope! ✨✨

is -1 bigger than 0.7

PLZ PLZ PLZ PLZ HELP ME WITH THIS QUESTION

Tell which number is greater.
80%,
17
9
is greater.

What is 8.478 in expanded form?

Will mark brainliest! Determine whether the rectangles are similar. If so, write the similarity
ratio and a similarity statement.

if f(x)=x²-18x+91, solve for x when f(x)=10​

How many cats and how many dog were adopted that weekend