Question

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.

Answer 1

Recall the following identities:

`\begin{gathered} \tan (t)=(\sin (t))/(\cos (t)) \\ \csc (t)=(1)/(\sin (t)) \\ \sec (t)=(1)/(\cos (t)) \\ \cot (t)=(\cos (t))/(\sin (t)) \end{gathered}`

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

`\begin{gathered} \tan (t)=(((12)/(13)))/(((5)/(13))) \\ =(12)/(5) \end{gathered}`
`\begin{gathered} \csc (t)=(1)/(((12)/(13))) \\ =(13)/(12) \end{gathered}`
`\begin{gathered} \sec (t)=(1)/(((5)/(13))) \\ =(13)/(5) \end{gathered}`
`\begin{gathered} \cot (t)=(((5)/(13)))/(((12)/(13))) \\ =(5)/(12) \end{gathered}`