If cot x = -5/12, x lies in second quadrant find the values of other five trigonometric functions

Given that \(\cot x = -\frac{5}{12}\) and \(x\) lies in the second quadrant, we need to find the values of the other five trigonometric functions: \(\sin x\), \(\cos x\), \(\tan x\), \(\sec x\), and \(\csc x\).

### Step 1: Use the cotangent identity

\[
\cot x = \frac{\cos x}{\sin x}
\]

Given \(\cot x = -\frac{5}{12}\), we can write:

\[
\frac{\cos x}{\sin x} = -\frac{5}{12}
\]

### Step 2: Express \(\cos x\) and \(\sin x\) using a right triangle

We can let \(\cos x = -5k\) and \(\sin x = 12k\) for some positive

Discover how to find trigonometric function values when given that cotangent \( \cot x = -\frac{5}{12} \) and \( x \) lies in the second quadrant. Explore step-by-step solutions using trigonometric identities and right triangle trigonometry. Suitable for Grades 11-12.

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