Solve the given trigonometric equation on 0^∘ ≤θ<360^∘ and express the answer in degrees to two

step 1 In this video, we will find the value of theta, given the equation, cosine of two theta is equal

Solve the given trigonometric equation on 0^∘ ≤θ<360^∘ and...

Key Concepts

Trigonometric Equations

Trigonometric equations involve finding the values of the variable (usually an angle) that satisfy an equation containing trigonometric functions. Solving these equations often requires the use of algebraic manipulation, trigonometric identities, and an understanding of the periodic properties of trigonometric functions.

Periodic Properties of Cosine

The cosine function has a period of 360° (or 2? radians), meaning that its values repeat every full rotation around the unit circle. This periodicity is crucial when solving cosine equations since it usually leads to an infinite number of solutions. However, the solutions are often restricted to a specified interval, requiring the identification of all solutions within that interval.

Inverse Trigonometric Functions

The inverse cosine function (cos?¹) is used to find the principal value of an angle given a cosine value. It provides the basic solution, which is then adjusted using the symmetry and periodicity of the cosine function to find all valid solutions within a given domain.

Double-Angle Equations

In equations where the trigonometric function involves a multiple of the variable (such as cos(2?)), the problem is a double-angle equation. This requires solving for the multiple variable first and then dividing by the corresponding factor to determine the solution for the original variable. Understanding this process is crucial for correctly addressing the transformed domain and obtaining all possible solutions.

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