Respuesta :
Answer:
[tex] \frac{7}{25} [/tex]
Step-by-step explanation:
We can solve that using this identity,
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
plug in -24/25 from x in sin
[tex] \sin {}^{2} ( \frac{ - 24}{25} ) + \cos {}^{2} (x) = 1[/tex]
[tex] \sin( \frac{576}{625} ) + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{576}{625} [/tex]
[tex] \cos {}^{2} (x) = \frac{49}{625} [/tex]
[tex] \cos(x) = \frac{7}{25} [/tex]
Since cos is positve in quadrant 4, the answer is 7/25.
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
then
Sin(Ф) = - [tex]\frac{24}{25}[/tex]
find the angle Ф
Ф = arcSin ( - [tex]\frac{24}{25}[/tex] )
Ф = -73.739795°
so an angle measured clock wise from x axis at zero°
now use cos(Ф) = x/ 25 to find x
25* cos( -73.739795°) = x
7 = x :o wow... exactly? :P nice
cos(Ф) = 7/25 I think that's what they wanted to know
also I noted my calculator tried to find the fraction of 0.2800000049 and couldn't, but then I just put in 0.28 and it found that to be 7/25 :0 so I think we're spot on :)
