Mathematics

Question

Given tan theta = -2 and pi/2 < theta < pi; find cos2theta.
a. - 4/3
b.- 4/5
c. 3/4
d. - 3/5

PLEASE HELP ASAP

1 Answer

  • Answer:

    Cos 2theta = -3/5

    Step-by-step explanation:

    Given that;

    tan theta = -2

    tan theta = -2/1 = opp/adj

    hyp^2 = (-2)^2+1^2

    hyp = √4+1

    hyp = √5

    sin theta = opp/hyp

    sin theta = -2/√5

    Cos theta = adj/hyp

    Cos theta = -2/√5

    Cos 2theta = 1-2sin^2 theta

    Cos 2theta = 1- 2(-2/√5)^2

    Cos 2theta = 1- 2(4/5)

    Cos 2theta = 1- 8/5

    Cos 2theta = (5-8)/5

    Cos 2theta = -3/5

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