Question

Solve the trigonometric equation in degrees. Check your quadrants and mode.

Answer 1

Explanation:

To solve the equation 9 + 3 * cos(θ) = 7, we can start by isolating the cosine term:

3 * cos(θ) = 7 - 9 3 * cos(θ) = -2

Now, to find the value of θ, we need to consider the given condition that tan(θ) > 0. The tangent function is positive in the first and third quadrants of the unit circle. Since the cosine function is negative in the second and third quadrants, we can conclude that θ lies in the third quadrant.

In the third quadrant, cos(θ) is negative. Therefore, to satisfy the equation 3 * cos(θ) = -2, we can take the cosine inverse (arccos) of both sides:

θ = arccos(-2/3)

Since θ lies in the third quadrant, the value of θ will be between 180 and 270 degrees (or between π and 3π/2 radians).

Hope it help you