Math / Trigonometry

QuestionQuestion Given that $\cot (x)=-\frac{5}{2}$ , what is $\cot (-x)$ ?
Provide your answer below:

Studdy Solution

STEP 1

1. We are given that $\cot(x) = -\frac{5}{2}$ .
2. We need to find the value of $\cot(-x)$ .

STEP 2

1. Recall the identity for the cotangent of a negative angle.
2. Apply the identity to find $\cot(-x)$ .

STEP 3

Recall the identity for the cotangent of a negative angle:
The identity is $\cot(-x) = -\cot(x)$ .

STEP 4

Apply the identity to find $\cot(-x)$ :
Since $\cot(x) = -\frac{5}{2}$ , we substitute into the identity:
$\cot(-x) = -\cot(x) = -\left(-\frac{5}{2}\right)$
Simplify the expression:
$\cot(-x) = \frac{5}{2}$
The value of $\cot(-x)$ is:
$\boxed{\frac{5}{2}}$

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