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Readme [11.4K]
3 years ago
9

Given that tan 0=-4/7 , and 270 degrees <0<360 degrees , what is the exact value of sec0?

Mathematics
1 answer:
Elanso [62]3 years ago
6 0
I take it you meant θ angle, anyway.

we know the tan(θ) = -4/7... alrite, we also know that 270° < θ < 360°, which is another to say that θ is in the IV quadrant, where the adjacent side or "x" value is positive whilst the opposite side or "y" value is negative.

\bf tan(\theta )=\cfrac{\stackrel{opposite}{-4}}{\stackrel{adjacent}{7}}\impliedby \textit{now let's find the \underline{hypotenuse}}&#10;\\\\\\&#10;\textit{using the pythagorean theorem}&#10;\\\\&#10;c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}&#10;\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}&#10;\\\\\\&#10;c=\sqrt{7^2+(-4)^2}\implies \implies c=\sqrt{65}\\\\&#10;-------------------------------\\\\&#10;sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{65}}}{\stackrel{adjacent}{7}}
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