Calculus Examples

$lim_{θ \to \frac{3 π}{2}} \sin (\tan (\cos (θ)))$

Step 1

Evaluate the limit.

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Step 1.1

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

$\sin (lim_{θ \to \frac{3 π}{2}} \tan (\cos (θ)))$

Step 1.2

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

$\sin (\tan (lim_{θ \to \frac{3 π}{2}} \cos (θ)))$

Step 1.3

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

$\sin (\tan (\cos (lim_{θ \to \frac{3 π}{2}} θ)))$

Step 2

Evaluate the limit of $θ$ by plugging in $\frac{3 π}{2}$ for $θ$ .

$\sin (\tan (\cos (\frac{3 π}{2})))$

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.

$\sin (\tan (\cos (\frac{π}{2})))$

Step 3.2

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\sin (\tan (0))$

Step 3.3

The exact value of $\tan (0)$ is $0$ .

$\sin (0)$

Step 3.4

The exact value of $\sin (0)$ is $0$ .

$0$