If sin θ = 1/√2, find cosec² θ

Tunajua kwamba $\text{cosec} \theta$ ni kinyume cha $\sin \theta$.

$$\text{cosec} \theta = \frac{1}{\sin \theta}$$

Umepewa $\sin \theta = \frac{1}{\sqrt{2}}$.

$$\text{cosec} \theta = \frac{1}{\frac{1}{\sqrt{2}}}$$ $$\text{cosec} \theta = \sqrt{2}$$

Sasa, tunahitaji kupata $\text{cosec}^2 \theta$.

$$\text{cosec}^2 \theta = (\sqrt{2})^2$$ $$\text{cosec}^2 \theta = 2$$

Thamani ya $\text{cosec}^2 \theta$ ni $\boxed{2}$.