3Square root of 2 cosine theta equals -1
To solve the equation 3√2 cos(theta) = -1, we can start by isolating the cosine term.
First, divide both sides of the equation by 3√2:
(3√2 cos(theta))/(3√2) = -1/(3√2)
This simplifies to:
cos(theta) = -1/(3√2)
Now, to find the value of theta, we need to apply the inverse cosine function (also known as arccosine or cos^(-1)) to both sides of the equation. This will give us the angle whose cosine is equal to -1/(3√2):
cos^(-1)(cos(theta)) = cos^(-1)(-1/(3√2))
Simplifying further:
theta = cos^(-1)(-1/(3√2))
To find the numerical value of theta, we can use a calculator or mathematical software that has the function cos^(-1) (also denoted as acos or arc cos) to compute the inverse cosine of -1/(3√2).