Trigonometry Examples

$\sin (\frac{π}{2} + \frac{π}{4})$

Step 1

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sin (\frac{π}{2} \cdot \frac{2}{2} + \frac{π}{4})$

Step 2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.1

Multiply $\frac{π}{2}$ by $\frac{2}{2}$ .

$\sin (\frac{π \cdot 2}{2 \cdot 2} + \frac{π}{4})$

Step 2.2

Multiply $2$ by $2$ .

$\sin (\frac{π \cdot 2}{4} + \frac{π}{4})$

Step 3

Combine the numerators over the common denominator.

$\sin (\frac{π \cdot 2 + π}{4})$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Move $2$ to the left of $π$ .

$\sin (\frac{2 \cdot π + π}{4})$

Step 4.2

Add $2 π$ and $π$ .

$\sin (\frac{3 π}{4})$

Step 5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (\frac{π}{4})$

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.70710678 \dots$