cos u = − 12 /13 , π/ 2 < u < π

Question

Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.

cos u = −  12 /13 ,      π/ 2  < u < π

Answer 1

cos u = −  12 /13,  π/ 2  < u < π

u is in second quadrant.

In second quadrant sin u is positive.

Adjacent side = 12 and Hypotenuse = 13

Find the opposite side:

opposite side = sqrt( 13^2 - 12^2 ) = 5

sin u = Opposite side / Hypotenuse

sin u = 5 /13

Double-angle formulas : sin 2u = 2 sin u cos u

sin 2u = 2 (5/13) (-12/13)

          = - 120 / 169

Answer 2

Step 1:

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Double-angle formula :.

Substitute .

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Solution:

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Answer 3

Step 1:

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Double-angle formula :.

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Substitute and .

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Substitute in .

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Solution:

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