Calculus Examples

$f (\frac{π}{2}) = 3 \sin (3 x)$

Step 1

Replace the variable $x$ with $\frac{π}{2}$ in the expression.

$f (\frac{π}{2}) = 3 \sin (3 (\frac{π}{2}))$

Step 2

Simplify the result.

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Step 2.1

Combine $3$ and $\frac{π}{2}$ .

$f (\frac{π}{2}) = 3 \sin (\frac{3 π}{2})$

Step 2.2

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.

$f (\frac{π}{2}) = 3 (- \sin (\frac{π}{2}))$

Step 2.3

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$f (\frac{π}{2}) = 3 (- 1 \cdot 1)$

Step 2.4

Multiply $3 (- 1 \cdot 1)$ .

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Step 2.4.1

Multiply $- 1$ by $1$ .

$f (\frac{π}{2}) = 3 \cdot - 1$

Step 2.4.2

Multiply $3$ by $- 1$ .

$f (\frac{π}{2}) = - 3$

Step 2.5

The final answer is $- 3$ .

$- 3$

Step 3