How would you solve:
5 cos x + 2 = 0
In the domain of 0 degrees to 360 degrees
5 cos x + 2 = 0
5 cos x = -2
cos x= -2/5
arccos (-2/5) = answer (check to see if you are supposed to answer in degrees or radians - change calculator settings accordingly)
also recall that cos(x) is negative in QII and QIII
Cos x = -0.40
X = 113.6o
To solve the equation 5 cos x + 2 = 0 in the domain of 0 degrees to 360 degrees, you need to isolate the variable x. Here's how you can do it:
Step 1: Subtract 2 from both sides of the equation:
5 cos x = -2
Step 2: Divide both sides of the equation by 5:
cos x = -2/5
Step 3: Find the reference angle using the inverse cosine function. Since the range of the inverse cosine function is restricted to 0 to 180 degrees (or 0 to π radians), we will look for solutions in this range.
cos⁻¹(-2/5) ≈ 116.565 degrees
Step 4: Determine the values of x within the given domain by considering both the positive and negative solutions. Since cosine is an even function, the cosine values are positive in the first and fourth quadrants. Hence, the solutions are:
x = 116.565 degrees
and
x = 360 degrees - 116.565 degrees = 243.435 degrees
Therefore, the solutions within the given domain are x = 116.565 degrees and x = 243.435 degrees.