Trigonometry Examples

$2 \sec^{2} (180) + \sin^{2} (0) + 4 \cos (180)$

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. Make the expression negative because secant is negative in the second quadrant.

$2 {(- \sec (0))}^{2} + \sin^{2} (0) + 4 \cos (180)$

Step 1.2

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

$2 {(- 1 \cdot 1)}^{2} + \sin^{2} (0) + 4 \cos (180)$

Step 1.3

Multiply $- 1$ by $1$ .

$2 {(- 1)}^{2} + \sin^{2} (0) + 4 \cos (180)$

Step 1.4

Raise $- 1$ to the power of $2$ .

$2 \cdot 1 + \sin^{2} (0) + 4 \cos (180)$

Step 1.5

Multiply $2$ by $1$ .

$2 + \sin^{2} (0) + 4 \cos (180)$

Step 1.6

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

$2 + 0^{2} + 4 \cos (180)$

Step 1.7

Raising $0$ to any positive power yields $0$ .

$2 + 0 + 4 \cos (180)$

Step 1.8

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.

$2 + 0 + 4 (- \cos (0))$

Step 1.9

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

$2 + 0 + 4 (- 1 \cdot 1)$

Step 1.10

Multiply $4 (- 1 \cdot 1)$ .

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Step 1.10.1

Multiply $- 1$ by $1$ .

$2 + 0 + 4 \cdot - 1$

Step 1.10.2

Multiply $4$ by $- 1$ .

$2 + 0 - 4$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $2$ and $0$ .

$2 - 4$

Step 2.2

Subtract $4$ from $2$ .

$- 2$