Mathematics: Solve using the Pythagorean identity

They should wake up at 11:55 to be at the air port on time 45+30= 1.15 hours.minuets 1:10-1.15: 11:55...

Solve using the Pythagorean identity

perlamaria01

24.07.2021

$\bold{Sin\theta_{1}=-\frac{4}{5}}$

Solution given

Cos $\displaystyle \theta_{1}=\frac{3}{5}$

consider Pythagorean theorem

$\bold{Sin²\theta+Cos²\theta=1}$

Subtracting $Cos²\theta$ both side

$\displaystyle Sin²\theta=1-Cos²\theta$

doing square root on both side we get

$Sin\theta=\sqrt{1-Cos²\theta}$

Similarly

$Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}$

Substituting value of $Cos\theta_{1}$

we get

$Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}$

Solving numerical

$Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}$

$Sin\theta_{1}=\sqrt{\frac{16}{225}}$

$Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}$

$Sin\theta_{1}=\frac{4}{5}$

Since

In IVquadrant sin angle is negative

$\bold{Sin\theta_{1}=-\frac{4}{5}}$

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