Sin(3pi over 4) = _____

1 answer:

8 0

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______________

$\mathsf{sin\!\left(\dfrac{3\pi}{4}\right)}\\\\\\ =\mathsf{sin\!\left(\dfrac{3\cdot 180^\circ}{4}\right)}\\\\\\ =\mathsf{sin(135^\circ)}\\\\ =\mathsf{sin(180^\circ-135^\circ)}$

$=\mathsf{sin(45^\circ)}\\\\ =\mathsf{\dfrac{\sqrt{2}}{2}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps.=)

Tags: sine sin common angles trig trigonometry

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If 1/√a-√b=1/3 and 1/√a+√b=1/2, then find the difference of a and b.

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If $\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{1}{3}$ and $\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{2}$ then the difference of a and b is 6

SOLUTION:

Given, $\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{1}{3}$ → $\sqrt{a}-\sqrt{b}=3$ ----- (1)

And $\frac{1}{\sqrt{a}+\sqrt{b}}=\frac{1}{2}$ → $\sqrt{a}+\sqrt{b}=2$ --- (2)

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$\sqrt{a}+\sqrt{b}=2$

Adding above two equations, we get,

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$\begin{array}{l}{2 \sqrt{a}=5} \\\\ {\sqrt{a}=\frac{5}{2}} \\\\ {a=\frac{25}{4}}\end{array}$

substitute $\sqrt{a}$ value in (2)

$\begin{array}{l}{\frac{5}{2}+\sqrt{b}=2} \\\\ {\sqrt{b}=\frac{2}{\sin \frac{5}{2}}} \\\\ {\sqrt{b}=\frac{4-5}{2}} \\\\ {\sqrt{b}=\frac{-1}{2}} \\\\ {b=\frac{1}{4}}\end{array}$