Question

Write the following expression in terms of the first power of the sine only. sin z + cos z

I am also having trouble with this one. Please help!

Answer 1

y=sqrt(2)sin(x+pi/4)

Answer 2

How did you solve this?

Answer 3

replaces cosz with sqrt(1-sin^2(z))

Answer 4

then add the two sins together and get 2 sin x? how did you know to add π/4?

Answer 5

sorry wrong approach to do tht, lemme start over

Answer 6

sin(90-x)=cosx

Answer 7

sin(pi/2-x)=cosx

Answer 8

im so confused! i dont understand how to write it in terms of sine

Answer 9

um do you kno sin (a+b) , sin(a-b) formula?
if u do
then write cosz as sin(pi/2-z) and use the identity

Answer 10

oh wait i just looped u lol

Answer 11

lol. im trying to figure it out but its not going so well.

Answer 12

i just woke up im sorrygive me two minutes

Answer 13

ok

Answer 14

k i want u to imagine tht sinx+cosx is written as sinxcos(pi/4)+cosxsin(pi/4)
do u kno why chose pi/4, because sin(pi/4) and cos(pi/4) both =1. now we can rewrite
sinxcos(pi/4)+cosxsin(pi/4) as sin(pi/4+x)

Answer 15

i mean they sin(pi/4)=sqrt 2 /2 and same for cos god im sleepy lol

Answer 16

\[\sin(x)+\cos(x)=>\sin(x)*\cos(\pi/4)+\cos(x)\sin(\pi/4)\]

Answer 17

if im writing it is terms of sine then why would cosine still be there? that where im confused

Answer 18

sin(x)∗cos(π/4)+cos(x)sin(π/4)=1/sqrt(2)(sinx+cosx)

Answer 19

but it can also be written as
sin(x+pi/4)=1/sqrt(2) (sinx+cosx)

Answer 20

bring sqrt(2) to the left hand side, by multiplying both sides sqrt2,
and u get the answer =)

Answer 21

lemme kno what part u didnt get and ill reexplain

Answer 22

so the answer is sqrt(2) sin(x+π/4) = sins + cosx

Answer 23

does the sqrt(2) stay multiplied outside or do i multiply it to everything??

Answer 24

it stays outside

Answer 25

\[\sqrt(2) \sin(\pi/4 +x)\]

Answer 26

goodluck

Answer 27

thanks for your help!

Answer 28

medal?

Answer 29

not to be greedy or anything =P

Answer 30

ill give you one! but whats the answer? im still confused whats the work?

Answer 31

lol? i showed u the work