Question

The angle 01 is located in Quadrant IV, and sin(01) = -24/ 25 What is the value of cos(01)?​

Answer 1

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) = - $\frac{24}{25}$

find the angle Ф

Ф = arcSin ( - $\frac{24}{25}$ )

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  :)  

Answer 2

Answer:

$\frac{7}{25}$

Step-by-step explanation:

We can solve that using this identity,

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

plug in -24/25 from x in sin

$\sin {}^{2} ( \frac{ - 24}{25} ) + \cos {}^{2} (x) = 1$

$\sin( \frac{576}{625} ) + \cos {}^{2} (x) = 1$

$\cos {}^{2} (x) = 1 - \frac{576}{625}$

$\cos {}^{2} (x) = \frac{49}{625}$

$\cos(x) = \frac{7}{25}$

Since cos is positve in quadrant 4, the answer is 7/25.