Question

what is sin(theta-90)

Answer 1

use these 2 relations
\(\Large \sin (90-\theta ) = \cos \theta \\ \Large \sin(-\theta ) = -\sin \theta \)

Answer 2

could you say that sin(90-theta) is equal to sin(90)-sin(theta)?

Answer 3

no, it doesn't work that way
\(\sin (A+B) \ne \sin A+\sin B \\\Large \sin (A+B) = \sin A \cos B +\cos A \sin B\)

you can use this formula too

Answer 4

could you explain it to me???? i still don't really get it

Answer 5

sure,

see, we have the formula sin (90-theta) = cos theta

but we need sin (theta - 90)

so we do
\(\huge \sin (90-\theta) = \sin [-(90-\theta )]\)
got this step ?

Answer 6

i mean
\(\huge \sin (\theta-90) = \sin [-(90-\theta )]\)

Answer 7

yeah

Answer 8

good, so now we use \( \sin (-x)=-\sin x \)

so we get
\(\Large \sin [-(90-\theta)] = - \sin (90-\theta) = -\cos \theta\)
makes sense ?

Answer 9

oooooooohhhhh

Answer 10

thx!

Answer 11

so it could also work the other way around and say cos(theta-90)=-sintheta?

Answer 12

but
\(\Large \cos (-x) = \cos x\)

hence
\(\cos (90-\theta ) = \cos (\theta -90) = \sin \theta\)
:)

Answer 13

k thx again!

Answer 14

welcome ^_^
you seem to be new here ,

\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)