Trigonometry Examples

$4 \csc (270) + 3 \cos (180)$

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 cosecant is negative in the third quadrant.

$4 (- \csc (90)) + 3 \cos (180)$

Step 1.2

The exact value of $\csc (90)$ is $1$ .

$4 (- 1 \cdot 1) + 3 \cos (180)$

Step 1.3

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

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Step 1.3.1

Multiply $- 1$ by $1$ .

$4 \cdot - 1 + 3 \cos (180)$

Step 1.3.2

Multiply $4$ by $- 1$ .

$- 4 + 3 \cos (180)$

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.

$- 4 + 3 (- \cos (0))$

Step 1.5

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

$- 4 + 3 (- 1 \cdot 1)$

Step 1.6

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

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Step 1.6.1

Multiply $- 1$ by $1$ .

$- 4 + 3 \cdot - 1$

Step 1.6.2

Multiply $3$ by $- 1$ .

$- 4 - 3$

Step 2

Subtract $3$ from $- 4$ .

$- 7$