Trig - Sums and Differences of angles (1 Viewer)

Andy005 · Jun 8, 2017

if sinx = 2/3 and cosy = 3/4, find the exact value of

a) sin(x+y)

Thanks for the help

InteGrand · Jun 8, 2017

Andy005 said:
if sinx = 2/3 and cosy = 3/4, find the exact value of

a) sin(x+y)

Thanks for the help

$\noindent We have $\sin(x+y) = \underbrace{\sin x}_{= \frac{2}{3}} \underbrace{\cos y}_{= \frac{3}{4}} + \cos x \sin y$.$

$\noindent We know the values of $\sin x$ and $\cos y$. From the given information alone, we can only pin down the value of $\cos x$ and $\sin y$ up to a $\pm$ sign (using the Pythagorean trig. identity).$

Andy005 · Jun 8, 2017

So what am I supposed to do exactly?

I'm just unsure on what to do after 1/2 + cosxsiny, i just need a hint in the right direction.

Thanks

Drongoski · Jun 8, 2017

$\therefore cos x = \sqrt{1-sin^2 x} = \sqrt {(1 - (\frac {2}{3})^2)} = \frac {\sqrt 5}{3}\\ \\ sin y = \sqrt{1 - cos^2 y} = \sqrt {1 - (\frac {3}{4})^2} = \frac {\sqrt 7}{4}\\ \\ \therefore sin(x+y) = sinx \cdot cos y + cosx \cdot siny = \frac{2}{3}\cdot \frac {3}{4} + \frac {\sqrt 7}{4} \cdot\frac {\sqrt 5}{3} = \frac {6 + \sqrt {35}}{12}$

Is my answer correct, Andy ??

Andy005 · Jun 8, 2017

Trig - Sums and Differences of angles (1 Viewer)

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