Question

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

Answer 1

Explanation:

• cos θ = 2/3

`\quad \twoheadrightarrow\sf {cos \; \theta = (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 = √(5)} \\`

Now, we know that :

`\quad \twoheadrightarrow\sf {cosec \; \theta = (Hypotenuse)/(Perpendicular) } \\`

`\quad \twoheadrightarrow\bf{cosec \; \theta = (3)/(√(5)) } \\`

Therefore, the required answer is 3/√5.