Trigonometry Examples

$\sin (45) \cos (180)$

Step 1

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cos (180)$

Step 2

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.

$\frac{\sqrt{2}}{2} (- \cos (0))$

Step 3

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

$\frac{\sqrt{2}}{2} (- 1 \cdot 1)$

Step 4

Combine fractions.

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Step 4.1

Multiply $- 1$ by $1$ .

$\frac{\sqrt{2}}{2} \cdot - 1$

Step 4.2

Combine $\frac{\sqrt{2}}{2}$ and $- 1$ .

$\frac{\sqrt{2} \cdot - 1}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Move $- 1$ to the left of $\sqrt{2}$ .

$\frac{- 1 \cdot \sqrt{2}}{2}$

Step 5.2

Rewrite $- 1 \sqrt{2}$ as $- \sqrt{2}$ .

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

Step 6

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.70710678 \dots$