Respuesta :

[tex] \frac{ \pi }is the 45 degree angle. the whole circle is 2π. so the positive angle is π/4+2π =\frac{9 \pi }{4} [/tex]
 the the negative angle is -(2π-π/4)= -\frac{7 \pi }{4}  

Answer:  The positive co-terminal angle is [tex]\dfrac{9\pi}{4}.[/tex] and the negative co-terminal angle is [tex]-\dfrac{7\pi}{4}.[/tex]

Step-by-step explanation:  We are to find the measures of the two angles, one positive and one negative, that are co-terminal with pi divided by four.

We know that

any two co-terminal angles differ from each other by an integral multiple of [tex]2\pi.[/tex]

So, to find the positive co-terminal angle, we will add [tex]2\pi[/tex] to [tex]\dfrac[\pi}{4}[/tex] and to find the negative co-terminal angle, we will subtract [tex]2\pi[/tex] from [tex]\dfrac[\pi}{4}[/tex].

Therefore, the required positive co-terminal angle is given by

[tex]C_p=\dfrac{\pi}{4}+2\pi=\dfrac{\pi+8\pi}{4}=\dfrac{9\pi}{4}.[/tex]

And, the required negative co-terminal angle is given by

[tex]C_n=\dfrac{\pi}{4}-2\pi=\dfrac{\pi-8\pi}{4}=-\dfrac{7\pi}{4}.[/tex]

Thus, the positive co-terminal angle is [tex]\dfrac{9\pi}{4}.[/tex] and the negative co-terminal angle is [tex]-\dfrac{7\pi}{4}.[/tex]

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