Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

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

Step 1.2

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

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

Step 1.3

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

$1 - \cot (\frac{7 π}{2})$

Step 1.4

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

$1 - \cot (\frac{3 π}{2})$

Step 1.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cotangent is negative in the fourth quadrant.

$1 - - \cot (\frac{π}{2})$

Step 1.6

The exact value of $\cot (\frac{π}{2})$ is $0$ .

$1 - - 0$

Step 1.7

Multiply $- - 0$ .

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Step 1.7.1

Multiply $- 1$ by $0$ .

$1 - 0$

Step 1.7.2

Multiply $- 1$ by $0$ .

$1 + 0$

Step 2

Add $1$ and $0$ .

$1$