Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as cos⁻¹ (arccos), are used to find the angle whose cosine is a given value. For example, if y = cos⁻¹(x), then cos(y) = x. These functions are defined within specific ranges to ensure they are one-to-one, which is crucial for determining unique angle values.
Recommended video:
Introduction to Inverse Trig Functions
Range of the Arccosine Function
The range of the arccosine function, cos⁻¹(x), is from 0 to π radians (or 0 to 180 degrees). This means that when you find the angle whose cosine is a specific value, the result will always fall within this interval, which is important for identifying valid solutions.
Recommended video:
Domain and Range of Function Transformations
Cosine Values
The cosine function outputs values between -1 and 1 for real angles. Specifically, cos(π) = -1, which is the only angle in the range of the arccosine function that corresponds to this value. Understanding the behavior of the cosine function helps in determining the exact angle when solving for y in the equation y = cos⁻¹(-1).
Recommended video:
Sine, Cosine, & Tangent of 30°, 45°, & 60°