# The question asks for the exact value of the trigonometric function at the given real number: sin((3pi)/4)

Question
Trigonometric Functions
The question asks for the exact value of the trigonometric function at the given real number:
$$\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}$$

2021-02-13
Trigonometric formula:
$$\displaystyle{\sin{{\left(\pi-\theta\right)}}}={\sin{\theta}}$$
Solving the given trigonometric function.
$$\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}$$
$$\displaystyle={\sin{{\left(\pi-\frac{\pi}{{4}}\right)}}}$$
$$\displaystyle={\sin{{\left(\frac{\pi}{{4}}\right)}}}{\left\lbrace,'{\sin{{\left(\pi-\theta\right)}}}={\sin{\theta}}\right\rbrace}$$
$$\displaystyle=\frac{{1}}{\sqrt{{2}}}$$
The value of given trigonometric function is shown below.
$$\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}=\frac{{1}}{\sqrt{{2}}}$$

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