Question

Find the value of the trigonometric function
$\cot (-\frac{15\pi }{4})$.

Answer 1

$\cot (-\frac{15\pi }{4})$ = −$\cot \left(\frac{15\pi }{4}\right)$ {∵cot(−𝑥)=−cot⁡𝑥 }
= −$\cot \left(\frac{16\pi -\pi }{4}\right)$
= −$\cot (4\pi -\frac{\pi }{4})$
Values of cot⁡𝑥 repeat after an interval of 𝜋,
hence ignoring 4𝜋
∴ $\cot (-\frac{15\pi }{4})$ = −$\cot (-\frac{\pi }{4})$ = −$(-\left(\cot \frac{\pi }{4}\right))$
⇒$\cot (-\frac{15\pi }{4})$= cot $\frac{\pi }{4}$ = 1