)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.

b < c < a < d

Step-by-step explanation:

P.S - The exact question is -

Given - Suppose x is a real number with 0 < x < . Set a = sin( - x) ,                                    

             b = cos( + x) , c = sin( x - ) , d = cos(2 - 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( - x) , sin ( - x) )

C = ( cos( + x), sin ( + x) )

D = ( cos (2 - x) , sin (2 - x) )

As we have given that 0 < x <

⇒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 ( - x) = sin (x) = a

By seeing point C , we can say that

cos( + x) = -cos (x) = b

By seeing point C , we can say that

sin( x - ) = -sin(x) = c

By seeing point D , we can say that

cos(2 - 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

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

kjgfcvbjkl

step-by-step explanation:

sdfghjkl; vbnm,