Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as sin⁻¹(x) and cos⁻¹(x), are used to find angles when given a trigonometric ratio. For example, cos⁻¹(-1) gives the angle whose cosine is -1, which is π radians (or 180 degrees). Understanding these functions is crucial for evaluating expressions involving them.
Recommended video:
Derivatives of Other Inverse Trigonometric Functions
Cosine Function
The cosine function, denoted as cos(x), relates the angle x in a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is periodic and ranges from -1 to 1. Knowing the values of cosine at key angles (like 0, π/2, π, etc.) is essential for simplifying expressions involving cosine.
Recommended video:
Graph of Sine and Cosine Function
Composition of Functions
Composition of functions involves applying one function to the result of another. In this case, evaluating cos(cos⁻¹(-1)) means finding the cosine of the angle whose cosine is -1. This concept is fundamental in calculus and algebra, as it allows for the simplification of complex expressions by breaking them down into manageable parts.
Recommended video:
Evaluate Composite Functions - Special Cases