Which one of the following equations has solution 3π/4
a. arctan 1 = x
b. arcsin √2/2 = x
c. arccos (―√2 /2) = x

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan, arcsin, and arccos, are used to find angles when given a ratio of sides in a right triangle. For example, arctan(1) gives the angle whose tangent is 1, which corresponds to π/4 radians. Understanding these functions is crucial for solving equations that involve finding angles from given trigonometric values.

Unit Circle

The unit circle is a fundamental concept in trigonometry that defines the relationship between angles and coordinates in a circular context. Each angle corresponds to a point on the circle, where the x-coordinate represents the cosine and the y-coordinate represents the sine of the angle. Knowing the coordinates of key angles, such as 3π/4, helps in determining the values of trigonometric functions and their inverses.

Trigonometric Values at Key Angles

Certain angles, like π/4, π/3, and π/6, have well-known sine, cosine, and tangent values. For instance, sin(3π/4) equals √2/2 and cos(3π/4) equals -√2/2. Recognizing these values allows for quick identification of the correct inverse function that yields a specific angle, which is essential for solving the given equations.