Solve cos(x)=0.07 on 0≤x<2π

just pull out your calculator.

cos(1.50) = 0.07

Since cos x > 0 in QI and QIV, the other solution is 2π-1.50

To solve the equation cos(x) = 0.07 on the interval 0 ≤ x < 2π, we need to find the values of x that satisfy this equation.

Step 1: Take the inverse cosine (arccos) of both sides of the equation:
arccos(cos(x)) = arccos(0.07)

Step 2: Simplify:
x = arccos(0.07)

Step 3: Use a calculator or a trigonometric table to find the principal value of arccos(0.07).

By evaluating arccos(0.07), we find that it is approximately equal to 1.4711 radians.

Step 4: Since the given interval is 0 ≤ x < 2π, we need to check if the obtained value of x falls within this range.

In this case, 1.4711 radians is less than 2π (approximately 6.2832 radians), so it is a valid solution.

Therefore, the solution to the equation cos(x) = 0.07 on the interval 0 ≤ x < 2π is x ≈ 1.4711 radians, or approximately 84.26 degrees.