Question

If cosθ=2/3 find cscθ using identities. This is in quad. 1.

Answer 1

Step-by-step explanation:

• cos θ = 2/3

$\quad \twoheadrightarrow\sf {cos \; \theta = \dfrac{Base}{Hypotenuse} }$

Hence, base = 2 units and hypotenuse = 3 units.

$\quad \twoheadrightarrow\sf { H^2 = B^2 + P^2}$

$\quad \twoheadrightarrow\sf { P^2 = H^2 - B^2}$

$\quad \twoheadrightarrow\sf { P^2 = (3)^2 - (2)^2}$

$\quad \twoheadrightarrow\sf { P^2 = 9- 4}$

$\quad \twoheadrightarrow\bf { P = \sqrt{5}}$

Now, we know that :

$\quad \twoheadrightarrow\sf {cosec \; \theta = \dfrac{Hypotenuse}{Perpendicular} }$

$\quad \twoheadrightarrow\bf{cosec \; \theta = \dfrac{3}{\sqrt{5}} }$

Therefore, the required answer is 3/√5.