Question

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

Answer 1

Recall that:

`\csc \theta=(1)/(\sin\theta)\text{.}`

If:

`\sin \theta=-(2)/(3),`

then:

`\csc \theta=(1)/(-(2)/(3))\text{.}`

Simplifying the above result we get:

`\csc \theta=-(3)/(2)\text{.}`

Answer:

`\csc \theta=-(3)/(2)\text{.}`