Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
cos θ = 0.32
Use algebra technique to make arc-cos(0.32) then round the answer to the two decimal places, = 71.34. So cos(71.34) = 0.32
To solve the equation cos θ = 0.32, we can use the inverse cosine function (also known as arccos) to find the angle θ.
Step 1: Take the inverse cosine of both sides of the equation.
arccos(cos θ) = arccos(0.32)
Step 2: Use a calculator to evaluate the inverse cosine of 0.32.
θ = arccos(0.32)
Using a calculator, the value of arccos(0.32) is approximately 1.239 radians, or approximately 71.08 degrees.
Therefore, the solution to the equation cos θ = 0.32 is θ = 1.239 (or 71.08 degrees).
To solve the equation cos θ = 0.32, we need to find the values of θ that satisfy this equation.
Step 1: Take the inverse cosine (also known as arccos) of both sides of the equation.
arccos(cos θ) = arccos(0.32)
Step 2: Simplify the left side. The inverse cosine function is the inverse of the cosine function, so they cancel out each other, returning us with just θ on the left side.
θ = arccos(0.32)
Step 3: Calculate the value of arccos(0.32). You can use a calculator or lookup tables to get the result.
θ ≈ 1.249 radians (or approximately 71.57 degrees)
Step 4: However, cosine is a periodic function, meaning it repeats itself every 2π radians (or 360 degrees). So to find all possible solutions, we need to add or subtract multiples of 2π.
θ ≈ 1.249 + 2πk, where k is any integer.
Therefore, the possible solutions for θ are approximately:
1.249 + 2πk, where k is any integer.