trig

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Given that tan B= 7/24 with B in quadrant III, find sin 2B, cos 2B, and tan 2B, using angle identities.

  • trig -

    Did you recognize the 7-24-25 right-angled triangle?
    then sin B = -7/25
    cos B = -24/25

    sin 2B = 2sinBcosB = 2(-7/25)(-24/25) = 336/625
    cos2B = cos^2B - sin^2B = 576/625- 49/625 = 527/625

    tan2B = sin2B/cos2B = (336/625)รท(527/625) = 336/527

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