Question

Find θ where 0 <= θ <= 2π for csc θ=(-2/√3)

Please answer in radian measure and without decimals, thank you

Answer 1

csc θ=(-2/√3)
or
sinθ= -√3/2 , where θ is in either III or IV

You should recognize the 30-60-90° triangle with corresponding sides of 1, √3, and 2
if sinθ = +√3/2, the θ = π/3 (60°)
so in quad III, θ = π + π/3 = 4π/3
and in IV, θ = 2π - π/3 = 5π/3

Answer 2

Thank you

Do you happen to know of any website or online tool hat I can use to test/graph this? I'm a visual learner and that would help a lot

Answer 3

Look at the "trig circle" in the top-right of the page.

https://www.google.ca/search?q=trig+circle+radians&rlz=1C6CHFA_enCA690CA691&sxsrf=ALeKk00eGYoXLNb1kxpyghssFekaiDJHjw:1590463648776&tbm=isch&source=iu&ictx=1&fir=7btvgKywl0C4yM%253A%252CPW_bt3de_fNtdM%252C_&vet=1&usg=AI4_-kR3sRiH6E_i9a_wW1ZzPOBKgIaIUw&sa=X&ved=2ahUKEwjmy8DmytDpAhWflHIEHeJhBC4Q_h0wAHoECAcQBA#imgrc=7btvgKywl0C4yM:

the ordered pairs are such that the x is the cosine of the angle and the y is the sine of the angle
e.g. for our problem , find our answers of θ = 4π/3 in quad III and in IV, θ = 5π/3
the y value of the ordered pairs will be -√3/2

If you click on the circle it will open a new page with some interesting stuff