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If y= cos x, what x-value corresponds to a y-value of 1/2 between pi and 2 pi

Sagot :

macintoshical101

Answer:

pi/3, 5pi/3

Step-by-step explanation:

We can see that when cosine is at 1/2, the angle measures are pi/3 degrees and 5pi/3 degrees. You can use a unit circle to find this. You can also find arccos(1/2), but that will only give you the value pi/3, not 5pi/3.

We can plug these in to find that they are indeed equal to 1/2.

loneguy

[tex]\text{Given that,}\\\\y =\cos x ~ \text{and}~ y =\dfrac 12\\\\\text{Now,}\\\\\cos x = \dfrac 12\\\\\implies x = 2n\pi \pm \dfrac{\pi}3\\\\\text{For interval}~ (\pi , 2\pi)\\\\x = \dfrac{5\pi}3 ~~ \text{or}~~ x =300^{\circ}[/tex]

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