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the angle t is an acute angle and sin t and cos t are given. use identities to find tan t, csc t, sec t, and cot t. where necessary, rationalizing denominators.

The Angle T Is An Acute Angle And Sin T And Cos T Are Given Use Identities To Find Tan T Csc T Sec T And Cot T Where Necessary Rationalizing Denominators class=

Sagot :

Recall the following identities:

[tex]\begin{gathered} \tan (t)=\frac{\sin (t)}{\cos (t)} \\ \csc (t)=\frac{1}{\sin (t)} \\ \sec (t)=\frac{1}{\cos (t)} \\ \cot (t)=\frac{\cos (t)}{\sin (t)} \end{gathered}[/tex]

Since sin(t)=12/13 and cos(t)=5/13, then:

[tex]\begin{gathered} \tan (t)=\frac{(\frac{12}{13})}{(\frac{5}{13})} \\ =\frac{12}{5} \end{gathered}[/tex][tex]\begin{gathered} \csc (t)=\frac{1}{(\frac{12}{13})} \\ =\frac{13}{12} \end{gathered}[/tex][tex]\begin{gathered} \sec (t)=\frac{1}{(\frac{5}{13})} \\ =\frac{13}{5} \end{gathered}[/tex][tex]\begin{gathered} \cot (t)=\frac{(\frac{5}{13})}{(\frac{12}{13})} \\ =\frac{5}{12} \end{gathered}[/tex]

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