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Sagot :
Answer:
[tex] \cos(x) = - \frac{5}{ \sqrt{41} } [/tex]
[tex] \csc(x) = \frac{ \sqrt{41} }{4} [/tex]
[tex] \tan(x) = - \frac{4}{5} [/tex]
Step-by-step explanation:
We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.
We need to find the cos, csc, and tan measure of this point.
We can find cos by using the formula of
[tex] \cos(x) = \frac{adj}{hyp} [/tex]
The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.
[tex] { - 5}^{2} + {4}^{2} = \sqrt{41} [/tex]
So using the info the answer is
[tex] \cos(x) = \frac{ - 5}{ \sqrt{41} } [/tex]
We can find tan but first me must find sin x.
[tex] \sin(x) = \frac{opp}{hyp} [/tex]
[tex] \sin(x) = \frac{4}{ \sqrt{41} } [/tex]
So now we just use this identity,
[tex] \tan(x) = \sin(x) \div \cos(x) [/tex]
[tex] \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} [/tex]
So tan x=
[tex] - \frac{ 4}{5} [/tex]
We can find csc by taking the reciprocal of sin so the answer is easy which is
[tex] \frac{ \sqrt{41} }{4} [/tex]
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