Rewrite in terms of sin(x) and cos(x). sin(x+[7pi/4])

in terms of sin(x) and cos(x) s

The expression is given as:

Using sine rule, we have:

So, the expression becomes

7π/4 is corresponding to π/4.

So, we have:

Evaluate the sine and the cosine of the angle

Factor out √2 / 2

Hence, the equivalent of is

Read more about trigonometry ratios at:

link

using the addition formulae for sin

• sin(x + y ) = sinxcosy + cosxsiny

sin (x + (7π/4))

= sinx cos (7π/4) + cosxsin (7π/4)

[ the related acute angle for 7π/4 is π/4 ]

= sinxcos (π/4) + cosx (- sin (π/4 )

= sinx × √2 / 2 - cosx × √2 /2

= √2 / 2(sinx - cosx )

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

7

step-by-step explanation:

the answer would be 7