Given that $\tan \beta = p$ and $180^\circ

Question

Given that $\tan \beta = p$ and $180^\circ < \beta < 270^\circ$, express each of the following in terms of $p$. $\cot \beta$ $\sin (-\beta)$ $\sec (270^\circ - \beta)$ $\sin (90^\circ - \beta)$ $\sec (\beta + 180^\circ)$ $\operatorname{cosec} (\beta - 90^\circ)$

Accepted Answer

(i) $\dfrac{1}{p}$; (ii) $-\dfrac{\sqrt{p^2 + 1}}{p^2 + 1}$; (iii) $\dfrac{p \sqrt{p^2 + 1}}{p^2 + 1}$; (iv) $\sqrt{p^2 + 1}$; (v) $\dfrac{\sqrt{p^2 + 1}}{p}$; (vi) $\sqrt{p^2 + 1}$

Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

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