Trigonometric formula for sin(x) + cos(x)?

Question

What is the formula, if any, for the above expression?

Answer 1

Pythagorean Identies

sin(x) + cos(x) = 1

- - - - - - - - - s-

Answer 2

If I'm not mistaken they would cancel each other out.

However in practical applications sin(x,y) and cos(x,y) where there is a fixed radius length and chaning x,y values to be in a realtionship with that is used in computer work to generate a circle on a monitor screen. It's a plotting tool.

240 A = 160
250 B = 80
260 R = 50
300 FOR ALPHA = 0 TO 360
310 X1 = INT(R * COS(ALPHA) + 0.5)
320 Y1 = INT(R * SIN(ALPHA) + 0.5)
330 PLOT A + X1, B + Y1
340 NEXT ALPHA

Answer 3

To use the same trigonometric line you have to pass to tan(x/2)
so sin x+ cos x=


((-tan^2(x/2)+2tan(x/2+1))
=_____________________
(1+tan^2(x/2)

Answer 4

i plot the graph of cos(x)+ sin (x), then it looks like cos(x) graph

so i changed the amplitutde my multiplying cos (x) with sq rt 2, then got sq rt 2 cos (x).

then after that i shift in the x domain and got smth like sq rt(2)cos (x-45degree).

i dunno y, but i think this is the answer

Answer 5

(sin x/ sec 2x) - (cos x / csc 2x) ==> sin x * cos 2x - cos x * sin 2x [theorem, sin(A (+-) B) = sin A cos B (+-) cos A sin B] ==> sin ( x - 2x ) ==> sin (-x) ==> - sin x [ it is also an rules if the angle of sine is negative then the negative sine can come before sine]

Answer 6

sinx + cosx = (length of side opp x + length of side adj x)/hypotenuse length

Answer 7

sinx=2sinx/2cosx/2
cosx=1-2sin*2(x/2)

if u want u can modify

sinx+cosx=cos2x/sinx-cosx

Answer 8

not any simple formula

Answer 9

sin(x) + cos(x) = sqrt(2) *sin(x+ (PI/4))

Answer 10

this is in simplest form but if you want in other form please let me know