Question

Assume that sin x =.8 and sin y =(square root(.75))
X and Y lie between 0 and ((pi)/2) Evaluate sin (x+y) Show all work Please?

Answer 1

sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
sin(x)=.8 therefore cos(x)= \[\sqrt{1-.8^{2}}\] = \[\sqrt{1-.64}=\sqrt{.36}=.6\]
sin(y)=root(.75) so
\[\cos(y)=\sqrt{1-\sqrt{.75}}=\sqrt{1-.75}=\sqrt{.25}=.5\]
both sine and cosine are positive because in quadrant 1.
hence
\[\sin(x+y)=\sin(x)\cos(y) + \cos(x)\sin(y)=.8\times.5+.6\times \sqrt{.75}\]

Answer 2

oops typo. \[\cos(y)=\sqrt{1-\sqrt{.75}^2}=\sqrt{1-.75}=\sqrt{.25}=.5\]

Answer 3

nostalgic?

Answer 4

wow

Answer 5

the good old days. before drawing
before "legend"
before wiggling icons

Answer 6

Ha! Not anymore, lol