Final answer:
To solve for real roots of a function involving cosine, utilize trigonometric identities and algebraic methods such as the quadratic formula, factoring, or substitution. Ensure that numerical solutions use radians for angles and check if answers are reasonable.
Step-by-step explanation:
To solve for real roots of a function involving cosine, one should typically utilize trigonometric identities and algebraic methods. If the function can be transformed into a quadratic-like equation using a trigonometric identity, then using the quadratic formula may be applicable. The factoring method could also be useful if the equation can be factored into simpler binomial or trinomial expressions. Lastly, if a simple substitution can be made to transform the trigonometric equation into an algebraic one, the substitution method can be employed.
For example, if we have a trigonometric function f(x) = cos(x) - x, we can make a list of the known facts about the function and the radians scale. We use numerical solutions and ensure they have the correct units when solving for the roots. Checking the reasonableness of the answer is also important to ensure that the solutions make sense within the context of the problem.
If one is unsure how to compute certain operations, such as square roots or trigonometric functions on a calculator, they should seek assistance from their instructor for proper guidance on these operations.