Question

if y = -cos x, what x-value corresponds to a y-value of 1 between 0 and 2π? ?π

Explanation:

Step1: Substitute y = 1 into the equation

We have the equation \( y = -\cos x \). Substitute \( y = 1 \) into it, so we get \( 1=-\cos x \).

Step2: Solve for \(\cos x\)

From \( 1 = -\cos x \), we can multiply both sides by -1 to get \( \cos x=- 1 \).

Step3: Find x in the interval \([0, 2\pi]\)

We know that the cosine function \( \cos x=-1 \) when \( x = \pi \) in the interval \([0, 2\pi]\) (since the cosine function has a period of \( 2\pi \) and \( \cos\pi=-1 \), \( \cos0 = 1 \), \( \cos2\pi=1 \) and for other values in between, we can recall the unit - circle definition of cosine: \( \cos\theta=x \) - coordinate of the point on the unit circle corresponding to angle \( \theta \), and the point corresponding to \( \theta=\pi \) is \((-1,0)\), so \( \cos\pi=-1\)). And we need to express \( x \) as \(?\pi \), so when \( x = \pi \), the coefficient of \( \pi \) is 1.

Answer:

1