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Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right-angled triangles. At its core, it involves studying patterns and functions like sine, cosine, and tangent, which are collectively known as trigonometric functions. These functions are crucial in various applications such as physics, engineering, astronomy, and even in art and music.

For students tackling trigonometry, a foundational understanding of how angles work and how they relate to the sides of triangles is essential. A key part of learning trigonometry is figuring out how to measure angles and use these measurements to calculate distances or predict the behavior of waves and cycles. It's a subject that blends abstract mathematical theory with real-world practicality.

Angles in the coordinate plane are measured from the positive x-axis, and as they increase, they travel counter-clockwise. The second quadrant is where angles land when they are greater than 90 degrees but less than 180 degrees. In trigonometry, the second quadrant holds particular significance because while the x-values (or cosines) of angles here are negative, the y-values (or sines) are positive.

Understanding the sign of trigonometric functions in this quadrant is crucial, especially when solving equations or verifying identities. When given an angle in the second quadrant, one should consider the implications this has for the corresponding trigonometric functions and reference angles, which leads us to the concept of angle measurement.

Angle measurement is a fundamental concept in both geometry and trigonometry. Angles are measured in either degrees or radians, and the measure of an angle corresponds to the amount of rotation one line, called the initial side, experiences to overlap with another line, called the terminal side. In trigonometry, being able to convert between degrees and radians, and understanding the unit circle, is essential.

One particular angle of interest is the 'reference angle.' This is the acute angle (less than 90 degrees) that is formed by the terminal side of an angle and the horizontal axis. Finding the reference angle is a common task when solving trigonometric problems because it simplifies calculations and helps to identify equivalent angles across different quadrants. For an angle in the second quadrant like 170 degrees, the reference angle is calculated as 180 degrees minus the given angle, yielding a simpler, acute reference angle with equivalent trigonometric function values.