Q. Find all angles, 0∘≤θ<360∘, that satisfy the equation below, to the nearest tenth of a degree.cos2θ−cosθ=0Answer: θ=
Identify Trigonometric Equation: First, let's identify the trigonometric equation we need to solve: cos2(θ)−cos(θ)=0. We can factor this equation to find the values of θ that satisfy it. Factor out cos(θ): cos(θ)(cos(θ)−1)=0. Now we have two factors that can be individually set to zero to find the solutions for θ.
Factor and Solve: Set the first factor equal to zero: cos(θ)=0. To find the angles where the cosine of θ is zero, we look at the unit circle. Cosine is zero at 90 degrees (π/2 radians) and 270 degrees (3π/2 radians).
Find Cosine Values: Set the second factor equal to zero: cos(θ)−1=0. Solve for cos(θ): cos(θ)=1. The angle where the cosine of θ is one is at 0 degrees (0 radians).
Solve for Theta: Now we have all the angles that satisfy the equation within the range of 0 to 360 degrees.The angles are 0 degrees, 90 degrees, and 270 degrees.Convert these angles to the nearest tenth of a degree, which in this case does not change the values since they are already whole numbers.
More problems from Find the roots of factored polynomials