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Use the fundamental identities to find the value of trigonometric function. Find csc θ, given that sin 2θ = - — and θ is in quadrant IV. 3

Sagot :

Recall that:

[tex]\csc \theta=\frac{1}{\sin\theta}\text{.}[/tex]

If:

[tex]\sin \theta=-\frac{2}{3},[/tex]

then:

[tex]\csc \theta=\frac{1}{-\frac{2}{3}}\text{.}[/tex]

Simplifying the above result we get:

[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]

Answer:

[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]

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