Alaina Valenzuela

2023-02-20

How to find the value of $\mathrm{tan}\left(-135°\right)$?

Determine the trigonometric ratio's value at the specified angle:
Let $x$ be the value of $\mathrm{tan}\left(-135°\right)$.
$\therefore x=\mathrm{tan}\left(-135°\right)$
$=-\mathrm{tan}135°$ $\left[\because tan\left(-a\right)=-ta\mathrm{na}\right]$
$=-\mathrm{tan}\left(1×90°+45\right)$
$=-\frac{\mathrm{sin}\left(90°+45°\right)}{\mathrm{cos}\left(90°+45°\right)}$ $\left[\because ta\mathrm{n\theta }=\frac{si\mathrm{n\theta }}{co\mathrm{s\theta }}\right]$
$=-\frac{\mathrm{cos}45°}{\left(-\mathrm{sin}45°\right)}$ $\left[\because sin\left(90°+a°\right)=cosa°;cos\left(90°+a°\right)=-sina°\right]$
$=\frac{\frac{1}{2}}{\frac{1}{2}}$ $\left[\because sin45°=\frac{1}{2};cos45°=\frac{1}{2}\right]$
$=1$
Hence, the value of $tan\left(-135°\right)$ is $1$.

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