If-3sin-x-4cos-y-3sin-y-8-then-sin-x-sin-y-

Question Number 173946 by mnjuly1970 last updated on 21/Jul/22

I f 3 s i n (x) + 4 c o s (y) - 3 s i n (y) = 8

t h e n . . s i n (x) + s i n (y) = ?

Answered by mr W last updated on 21/Jul/22

3 \sin x + 4 \cos y - 3 \sin y = 8

3 \sin x + 5 (\frac{4}{5} \cos y - \frac{3}{5} \sin y) = 8

3 \sin x + 5 (\cos α \cos y - \sin α \sin y) = 8

3 \sin x + 5 \cos (y + α) = 8

\Rightarrow \sin x = 1 \land \cos (y + α) = 1

\Rightarrow y + α = 2 k π

\Rightarrow y = 2 k π - α

\Rightarrow \sin y = - \sin α = - \frac{3}{5}

\Rightarrow \sin x + \sin y = 1 - \frac{3}{5} = \frac{2}{5} ✓

Commented by mathlove last updated on 22/Jul/22

w a y

\frac{4}{5} c o s y - \frac{3}{5} s i n y = s i n α c o s h - c o s α s i n y

Commented by infinityaction last updated on 22/Jul/22

3, 4, 5 i s a r i g h t a n g l e t r i a n g l e

Commented by Tawa11 last updated on 22/Jul/22

Great sir

Commented by mr W last updated on 22/Jul/22

f o r a n y v a l u e s a a n d b, w e c a n f i n d α

s u c h t h a t

\sin α = \frac{a}{\sqrt{a^{2} + b^{2}}}, \cos α = \frac{b}{\sqrt{a^{2} + b^{2}}} .

i n o u r c a s e : a = 3, b = 4 .

Commented by mnjuly1970 last updated on 22/Jul/22

v e r y n i c e s i r W