Precalculus Examples

$\sin (40) (\sin (180)) - \cos (40) \cos (180)$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (40) \sin (0) - \cos (40) \cos (180)$

Step 1.2

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

$\sin (40) \cdot 0 - \cos (40) \cos (180)$

Step 1.3

Multiply $\sin (40)$ by $0$ .

$0 - \cos (40) \cos (180)$

Step 1.4

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.

$0 - \cos (40) (- \cos (0))$

Step 1.5

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

$0 - \cos (40) (- 1 \cdot 1)$

Step 1.6

Multiply $- 1$ by $1$ .

$0 - \cos (40) \cdot - 1$

Step 1.7

Multiply $- \cos (40) \cdot - 1$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$0 + 1 \cos (40)$

Step 1.7.2

Multiply $\cos (40)$ by $1$ .

$0 + \cos (40)$

Step 2

Add $0$ and $\cos (40)$ .

$\cos (40)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\cos (40)$

Decimal Form:

$0.76604444 \dots$