Trig

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Find the exact value of sin2(theta) if cos(theta) = -sqrt 5/3 and 180 < theta < 270.
A)-1/9
B)-4 sqrt 5/9
C)1/9
D)4 sqrt 5/9
B?

sin^2(theta) + cos^2(theta) = 1
sin^2(theta) = 1 - cos^2(theta)
sin^2(theta) = 1 - (sqrt 5/3)^2
sin^2(theta) = 1 - (sqrt 25/9)

  • Trig -

    You are getting a lot of these wrong lately.

    (I am going to use sinx for your sin(theta)

    since cosx = √5 /3
    using Pythagoras I found the other side ot the triangle to be 2.
    But we are in the third quadrant so sinx =-2/3

    then sin 2x = 2sinxcosx
    = 2(-2/3)(-√5/3)
    = 4√5/3 which is D

    with a calculator, you could have easily checked that your choice and the others beside D would not work.

  • Trig -

    oops, sorry type

    make 4√5/3 which is D
    read : 4√5/9 which is D

  • Trig -

    I really thought I had that one.
    My 1st thought was D but I figured since sqrt 5/3 was negative then so would my final answer.

  • Trig -

    Are you familiar with the CAST rule, that is, do you know which ratios are negative in which quadrants??

  • Trig -

    No

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