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Mariulka [41]
2 years ago
8

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

Mathematics
1 answer:
laiz [17]2 years ago
4 0

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.

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