# Find tan 2 theta, sin theta = 7/25, theta lies in quadrant II

Find $\mathrm{tan}2\theta ,\mathrm{sin}\theta =7/25,\theta$ lies in quadrant II
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Sandra Randall
$\mathrm{tan}2x=2\mathrm{sin}x\mathrm{cos}x/{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x$
$\mathrm{cos}x=\sqrt{1-{\mathrm{sin}}^{2}x}$
substitute and obtain the value.

Paxton Hoffman
$\mathrm{tan}2x=2\mathrm{sin}x\mathrm{cos}x/{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x$
$\mathrm{cos}x=\sqrt{1-{\mathrm{sin}}^{2}x}$
substitute and obtain the value.
$\mathrm{tan}2\theta =\frac{2\mathrm{sin}\theta }{{\mathrm{cos}}^{2}\theta -{\mathrm{sin}}^{2}\theta }$
$\mathrm{cos}\theta =\sqrt{1-{\mathrm{sin}}^{2}2\theta }$
in this case $\theta \sim 0.28379$