Respuesta :

[tex]\bf csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -----------------------------\\\\ csc(135^o)\implies \cfrac{1}{sin(135^o)}\implies \cfrac{1}{\frac{\sqrt{2}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{2}}{2}}\implies \cfrac{1}{1}\cdot \cfrac{2}{\sqrt{2}}\implies \cfrac{2}{\sqrt{2}} \\\\\\ \textit{now, rationalizing the denominator} \\\\\\ \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{(\sqrt{2})^2}\implies \cfrac{2\sqrt{2}}{2}\implies \boxed{\sqrt{2}}[/tex]
okpalawalter8

The exact value of the expression csc 135° is mathematically given as

csc 135°=√2

What is the exact value of the expression is undefined csc 135°?

Question Parameter(s):

the expression is csc 135°

Generally, the equation for the expression is mathematically given as

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

therefore,

[tex]csc(135\textdegree)= \frac{1}{sin(135^o)}[/tex]

[tex]csc(135^ {\textdegree} )= \frac{1}{\frac{\sqrt{2}}{2}}[/tex]

[tex]csc(135 \textdegree)=\cfrac{1}{1}\cdot \frac{2}{\sqrt{2}}[/tex]

[tex]csc(135 \textdegree)= \frac{2}{\sqrt{2}}[/tex]

Now with the denominator rationalized

[tex]csc 135 \textdegree= \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]csc135 \textdegree = \cfrac{2\sqrt{2}}{(\sqrt{2})^2}[/tex]

Therefore, if the denominator becomes two, it divides the numerator by two and gives the resulting answer

csc 135°=√2

In conclusion, the exact value of [tex]csc 135 \textdegree[/tex]

csc 135°=√2

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