mooltattawsmq8

2022-12-28

Find the value of cos ${225}^{\circ}$

eyrurin3wj

Beginner2022-12-29Added 10 answers

Determining the worth of $\mathrm{cos}{225}^{\circ}$

$\mathrm{cos}{225}^{\circ}$ can be expressed as

$\mathrm{cos}{225}^{\circ}=\mathrm{cos}({180}^{\circ}+{45}^{\circ})$

$\Rightarrow $$\mathrm{cos}({180}^{\circ}+{45}^{\circ})=\mathrm{cos}{180}^{\circ}\times \mathrm{cos}{45}^{\circ}\u2013\mathrm{sin}{180}^{\circ}\times \mathrm{sin}{45}^{\circ}$ ; $\left[\mathrm{cos}(A+B)=\mathrm{cos}\left(A\right)\times \mathrm{cos}\left(B\right)-\mathrm{sin}\left(A\right)\times \mathrm{sin}\left(B\right)\right]$

When we substitute the above angles' values, we obtain,

$\mathrm{cos}{180}^{\circ}=-1,\mathrm{cos}{45}^{\circ}=\frac{2}{2},\mathrm{sin}{180}^{\circ}=0\mathrm{and}\mathrm{sin}{45}^{\circ}=\frac{2}{2}$

$\mathrm{cos}({180}^{\circ}+{45}^{\circ})=-1\times \left(\frac{2}{2}\right)-0\times \left(\frac{2}{2}\right)=-\frac{2}{2}=-\frac{1}{2}$

Thus the value of $\mathrm{cos}{225}^{\circ}$ is $-\frac{1}{2}$

$\mathrm{cos}{225}^{\circ}$ can be expressed as

$\mathrm{cos}{225}^{\circ}=\mathrm{cos}({180}^{\circ}+{45}^{\circ})$

$\Rightarrow $$\mathrm{cos}({180}^{\circ}+{45}^{\circ})=\mathrm{cos}{180}^{\circ}\times \mathrm{cos}{45}^{\circ}\u2013\mathrm{sin}{180}^{\circ}\times \mathrm{sin}{45}^{\circ}$ ; $\left[\mathrm{cos}(A+B)=\mathrm{cos}\left(A\right)\times \mathrm{cos}\left(B\right)-\mathrm{sin}\left(A\right)\times \mathrm{sin}\left(B\right)\right]$

When we substitute the above angles' values, we obtain,

$\mathrm{cos}{180}^{\circ}=-1,\mathrm{cos}{45}^{\circ}=\frac{2}{2},\mathrm{sin}{180}^{\circ}=0\mathrm{and}\mathrm{sin}{45}^{\circ}=\frac{2}{2}$

$\mathrm{cos}({180}^{\circ}+{45}^{\circ})=-1\times \left(\frac{2}{2}\right)-0\times \left(\frac{2}{2}\right)=-\frac{2}{2}=-\frac{1}{2}$

Thus the value of $\mathrm{cos}{225}^{\circ}$ is $-\frac{1}{2}$

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