Determine the value of cos(theta) given that cos(pi − theta) = .2

(A)
p.96 (B) .2 (C) −.2 (D) −p.96 (E) None of the above.

To determine the value of cos(theta), given that cos(pi - theta) = 0.2, we can use the cosine difference identity.

The cosine difference identity states that cos(pi - theta) = cos(pi) * cos(theta) + sin(pi) * sin(theta).

Since the cosine of pi is -1 and the sine of pi is 0, the equation simplifies to:
cos(pi - theta) = -1 * cos(theta) + 0 * sin(theta)
cos(pi - theta) = -cos(theta)

Now, we can substitute the given value into the equation:
0.2 = -cos(theta)

To find the value of cos(theta), we can solve for theta using inverse cosine (also known as arccos). Taking the inverse cosine of both sides, we get:

arccos(0.2) = arccos(-cos(theta))

Since the range of arccos is between 0 and pi, and the cosine function is an even function (symmetric about the y-axis), the only values that satisfy this equation are in the range [0, pi].

Therefore, we have:
theta = arccos(0.2)

Using a calculator, we can evaluate the inverse cosine of 0.2:
theta ≈ 1.369438406

Finally, we need to determine the value of cos(theta). Plugging our value of theta into the cosine function:

cos(theta) = cos(1.369438406)

Using a calculator, we can find that cos(theta) is approximately 0.200119.

Since the given value is rounded to one decimal place, we can conclude that the value of cos(theta) is approximately 0.2.

Therefore, the correct answer is (B) 0.2.