Algebra Examples

$\csc (- \frac{9 π}{2}) + \cot (- \frac{7 π}{4})$

Step 1

Simplify each term.

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Step 1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\csc (\frac{3 π}{2}) + \cot (- \frac{7 π}{4})$

Step 1.2

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 fourth quadrant.

$- \csc (\frac{π}{2}) + \cot (- \frac{7 π}{4})$

Step 1.3

The exact value of $\csc (\frac{π}{2})$ is $1$ .

$- 1 \cdot 1 + \cot (- \frac{7 π}{4})$

Step 1.4

Multiply $- 1$ by $1$ .

$- 1 + \cot (- \frac{7 π}{4})$

Step 1.5

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$- 1 + \cot (\frac{π}{4})$

Step 1.6

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$- 1 + 1$

Step 2

Add $- 1$ and $1$ .

$0$