Question #3acab

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Question #3acab

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Answer 1 · 2017-05-14T11:11:09

$see explanation$ $"see explanation"$

Explanation:

$using right triangle with a vertex at the origin and angle$ $"using right triangle with a vertex at the origin and angle "$
$θ, with sides corresponding to θ$ $theta," with sides corresponding to " theta$

$adjacent = x, opposite = y, hypotenuse = r$ $"adjacent "=x ," opposite " =y ," hypotenuse " =r$

$\Rightarrow sin θ = \frac{y}{r}, cos θ = \frac{x}{r} and r^{2} = x^{2} + y^{2}$ $rArrsintheta=y/r , costheta=x/r" and " r^2=x^2+y^2$

$\Rightarrow 1 - {sin}^{2} θ = 1 - \frac{y^{2}}{r^{2}} = \frac{r^{2}}{r^{2}} - \frac{y^{2}}{r^{2}}$ $rArr1-sin^2theta=1-y^2/(r^2)=r^2/(r^2)-y^2/(r^2)$

$\Rightarrow 1 - {sin}^{2} θ = \frac{r^{2} - y^{2}}{r^{2}} = \frac{x^{2}}{r^{2}} = {cos}^{2} θ$ $rArr1-sin^2theta=(r^2-y^2)/r^2=x^2/(r^2)=cos^2theta$

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Question #3acab

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