Trigonometry Examples

$3 \sec (180) - 5 \tan (360)$

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.

$3 (- \sec (0)) - 5 \tan (360)$

Step 1.2

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

$3 (- 1 \cdot 1) - 5 \tan (360)$

Step 1.3

Multiply $3 (- 1 \cdot 1)$ .

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Step 1.3.1

Multiply $- 1$ by $1$ .

$3 \cdot - 1 - 5 \tan (360)$

Step 1.3.2

Multiply $3$ by $- 1$ .

$- 3 - 5 \tan (360)$

Step 1.4

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$- 3 - 5 \tan (0)$

Step 1.5

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

$- 3 - 5 \cdot 0$

Step 1.6

Multiply $- 5$ by $0$ .

$- 3 + 0$

Step 2

Add $- 3$ and $0$ .

$- 3$