Find the best solutions to your problems with the help of IDNLearn.com's experts. Whether it's a simple query or a complex problem, our experts have the answers you need.
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.
