Given that $\sec \theta = -y$ and $\frac{\pi}{2}

Question

Given that $\sec \theta = -y$ and $\frac{\pi}{2} < \theta < \pi$, express each of the following in terms of $y$. $\cos \theta$ $\tan(-\theta)$ $\sec(\pi + \theta)$ $\sin(\theta - \pi)$ $\cot \left( \frac{\pi}{2} - \theta \right)$ $\text{cosec} \left( \theta - \frac{\pi}{2} \right)$

Accepted Answer

(i) $-\frac{1}{y} $ (ii) $ -\frac{\sqrt{y^2 - 1}}{y} $ (iii) $ \sqrt{y^2 - 1}$ (iv) $-\sqrt{y^2 - 1}$ (v) $y$ (vi) $y$

Trigonometry - Symmetry of Trigonometric Functions

Trigonometry - Symmetry of Trigonometric Functions

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