If =4 5 , find all other trigonometric rations of angle . - Vidyadip

Question

If $\cos\theta=\frac{4}{5},$ find all other trigonometric rations of angle $\theta$.

✓

Answer

We have $\sin\theta=\sqrt{1-\cos^2\theta}=\sqrt{1-\Big(\frac{4}{5}\Big)^2}$
$=\sqrt{1-\frac{16}{25}}$
$=\sqrt{25-\frac{16}{25}}$
$=\sqrt{\frac{9}{25}}=\frac{3}{5}$
$\therefore\ \sin\theta=\frac{3}{5}$
$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{3}{5}}{\frac{4}{5}}$
$=\frac{3}{4}\sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}}=\frac{5}{4}$
$\text{cosec}=\frac{1}{\sec\theta}=\frac{1}{\frac{3}{5}}$
$=\frac{5}{3}\cot\theta=\frac{1}{\tan\theta}=\frac{1}{\frac{3}{4}}=\frac{4}{3}$

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