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1 October, 05:59

If tan theta = 12/5 and cos theta < 0, what is sin theta?

a. 12

b. 5/13

c.-5/13

d. 12/13

e.-12/13

+2
Answers (1)
  1. 1 October, 09:39
    0
    1 + tan ² Ф=sec²Ф

    1 + (12/5) ²=sec²Ф

    169/25=sec² Ф

    sec Ф=⁺₋√ (169/25) = ⁺₋13/5

    sec Ф=1/cos Ф ⇒cosФ=1/sec Ф

    cos Ф>0 ⇔ sec Ф>0 ⇔ sec Ф = + 13/5

    cos Ф=1/secФ

    cos Ф=1 / 13/5=5/13

    we can calculate the sin Ф, with this method.

    sin²Ф + cos²Ф=1 ⇒ sin Ф=⁺₋√ (1-cos² Ф)

    sin Ф=⁺₋√[1 - (5/13) ²]=⁺₋12/13

    like cos Ф>0 and tan Ф>0 ⇒ sin Ф>0 ⇒sin Ф=12/13

    answer: d. 12/13

    other method

    tan Ф=sin Ф / cos Ф

    12/5=sin Ф / 5/13

    sin Ф = (12/5) * (5/13) = 12/13

    answer: d. 12/13
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