Question 1

Hi, I need help with my trigonometry hw. thank you

Question 2

Solution:

Given:

$f(t)=tan\text{ }t$
$\begin{gathered} when\text{ }t=-(\pi)/(2) \\ f(t)=tan(-(\pi)/(2)) \\ f(t)=undefined \\ \\ \\ when\text{ t}=-(\pi)/(3) \\ f\mleft(t\mright)=tan(-(\pi)/(3)) \\ f(t)=-√(3) \\ \\ \\ when\text{ t}=-(\pi)/(4) \\ f\mleft(t\mright)=tan(-(\pi)/(4)) \\ f(t)=-1 \\ \\ \\ when\text{ t}=-(\pi)/(6) \\ f\mleft(t\mright)=tan(-(\pi)/(6)) \\ f(t)=-(√(3))/(3) \end{gathered}$

$\begin{gathered} when\text{ }t=0 \\ f(t)=tan(0) \\ f(t)=0 \\ \\ \\ when\text{ t}=(\pi)/(6) \\ f\mleft(t\mright)=tan((\pi)/(6)) \\ f(t)=(√(3))/(3) \\ \\ \\ when\text{ t}=(\pi)/(4) \\ f\mleft(t\mright)=tan((\pi)/(4)) \\ f(t)=1 \\ \\ \\ when\text{ t}=(\pi)/(3) \\ f\mleft(t\mright)=tan((\pi)/(3)) \\ f(t)=√(3) \\ \\ \\ when\text{ t}=(\pi)/(2) \\ f\mleft(t\mright)=tan((\pi)/(2)) \\ f(t)=undefined \\ \\ \\ when\text{ t}=(2\pi)/(3) \\ f\mleft(t\mright)=tan((2\pi)/(3)) \\ f(t)=-√(3) \end{gathered}$

Therefore, the complete table is;

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