If 3sin(x)+4cos(y)−3sin(y)=8 then .. sin(x) + sin(y)=?


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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

	$v e r y n i c e s i r W$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum