Trigonometry Examples

$\sin (\frac{7 π}{6}) \cos (π) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 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 third quadrant.

$- \sin (\frac{π}{6}) \cos (π) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$- \frac{1}{2} \cos (π) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 3

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

$- \frac{1}{2} (- \cos (0)) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 4

The exact value of $\cos (0)$ is $1$ .

$- \frac{1}{2} (- 1 \cdot 1) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 5

Multiply $- 1$ by $1$ .

$- \frac{1}{2} \cdot - 1 - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 6

Multiply $- \frac{1}{2} \cdot - 1$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{2}) - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 6.2

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2} - \cos (\frac{7 π}{6}) \sin (\frac{π}{2})$

Step 7

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

$\frac{1}{2} - - \cos (\frac{π}{6}) \sin (\frac{π}{2})$

Step 8

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{1}{2} - - \frac{\sqrt{3}}{2} \sin (\frac{π}{2})$

Step 9

Multiply $- - \frac{\sqrt{3}}{2}$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{2} + 1 \frac{\sqrt{3}}{2} \sin (\frac{π}{2})$

Step 9.2

Multiply $\frac{\sqrt{3}}{2}$ by $1$ .

$\frac{1}{2} + \frac{\sqrt{3}}{2} \sin (\frac{π}{2})$

Step 10

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

$\frac{1}{2} + \frac{\sqrt{3}}{2} \cdot 1$

Step 11

Multiply $\frac{\sqrt{3}}{2}$ by $1$ .

$\frac{1}{2} + \frac{\sqrt{3}}{2}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2} + \frac{\sqrt{3}}{2}$

Decimal Form:

$1.36602540 \dots$