Solve for θ in the equation cos θ = -0.334 when 0º < θ < 180º. Round your answer to the nearest tenth of a degree.
between 90 and 180 where x is - and y is +
cos^-1 (.334) = 70.5
so 180 - 70.5 = 109.5
Thank you very much! I didn't know the formula.
To solve for θ in the equation cos θ = -0.334, we can use the inverse cosine function (arccos) which gives us the angle θ for a given cosine value.
First, we will find the principal value of θ by taking the inverse cosine of -0.334:
θ = arccos(-0.334)
Using a calculator or a mathematical software, we find:
θ ≈ 1.901 radians
To convert radians to degrees, we multiply by 180/π:
θ ≈ 1.901 * (180/π) ≈ 109.048 degrees
However, we are given the restriction that 0º < θ < 180º. To find the angle within this restriction that has the same cosine value, we use the fact that cosine function is negative in the second quadrant (90º < θ < 180º):
θ = 180 - 109.048 ≈ 70.952 degrees
Therefore, the solution to the equation cos θ = -0.334, within the given restriction, is approximately θ ≈ 70.952 degrees (rounded to the nearest tenth of a degree).