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How come cosine of 225 degrees is a positive number i thought it was negative because it's reference angle would be 45 degrees below the second quadrant and in a unit circle cosine is just the x value so I thought cosine of something in both the second and third were negative

apparently i'm wrong please explain

  • Trig -

    225º is in the fourth quadrant, 45º below the first quadrant, so its x value is indeed positive.
    Check how angles are measured.

  • Trig -

    I think i was in radians my bad

    um how come tan of 300 is negative root three

    tangent in unit circle is y/x I am getting .5/(root three/2)
    which is not root three

  • OOPS -Trig -

    Forget about my previous post.

    Obviously 225º is in the third quadrant, 45º below the second quadrant like you said.
    So of course cos 225 is negative.

  • Trig -

    tan 300º
    = -tan 60º by the CAST rule
    = -√3/1 from the ratios of the 30-60-90 triangle
    = -√3

  • Trig -

    why wouldn't you use the 30 degree angle?

    I did 360 -90 to get 270 degrees and then did 300 - 270 to get 30 degrees and used that angle why would I use the 60 degree angle instead of the thirty

  • Trig -

    Always ask yourself,
    "How far away from the x-axis am I "?
    to get the reference angle.

    e.g. sin 160
    160º is 20º away from the x-axis and according to the CAST rule in quadrant II the sine is positive, so
    sin 160º
    = sin 20º

    e.g. tan 310º
    310º is 50º from the x-axis and according to the CAST rule, in quadrant IV the tangent is negative, so
    tan 310
    = -tan 50

    check my examples with your calculator

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