Question

COSEC THEATA =ROOT 10, FIND ALL OTHER TRIGONOMETRIC RATIOS

Answer 1

Hope it will help you

Answer 2

Answer:

All trignometric ratios are

$sin\theta = \frac{1}{\sqrt{10}}$

$cos\theta = \frac{3}{\sqrt{10}}$

$tan\theta = \frac{1}{3}$

$cot\theta = \frac{3}{1}$

$sec\theta = \frac{\sqrt{10}}{3}$

Step-by-step explanation:

As by using the trignometric identity .

$cosec\theta = \frac{Hypotenuse}{Perpedicular}$

As given

$Cosec\theta = \sqrt{10}$

Thus compare the above terms .

Perpendicular = 1 unit

$Hypotenuse = \sqrt{10}\ unit$

By using the pythagoreams theorem

Hypotenuse² = Perpendicular² + Base²

$(\sqrt{10})^{2} = 1 + Base^{2}$

Base² = 10 - 1

Base² = 9

Base =√9

Base = 3 unit

Thus all trignometric ratios are

(1)$sin\theta = \frac{Perpedicular}{Hypotenuse}$

Putting values in the above

$sin\theta = \frac{1}{\sqrt{10}}$

(2)$cos\theta = \frac{Base}{Hypotenuse}$

Putting values in the above

$cos\theta = \frac{3}{\sqrt{10}}$

(3)$tan\theta = \frac{Perpedicular}{Base}$

Putting values in the above

$tan\theta = \frac{1}{3}$

(4)$cot\theta = \frac{Base}{Perpendicular}$

Putting values in the above

$cot\theta = \frac{3}{1}$

(5)$sec\theta = \frac{Hypotenuse}{Perpendicular}$

Putting values in the above

$sec\theta = \frac{\sqrt{10}}{3}$