Calculus Examples

$lim_{x \to \frac{7 π}{4}} \sin (x)$

Step 1

Move the limit inside the trig function because sine is continuous.

$\sin (lim_{x \to \frac{7 π}{4}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{7 π}{4}$ for $x$ .

$\sin (\frac{7 π}{4})$

Step 3

Simplify the answer.

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Step 3.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$- \sin (\frac{π}{4})$

Step 3.2

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{2}$

Decimal Form:

$- 0.70710678 \dots$