Trigonometry: Finding reference angles
This is a free lesson from our course in Trigonometry
 
   
This lesson introduce to the key concepts of reference angle and how to find the reference angle to a given angle. You'll learn with the help of several examples and explanation by instructor using video, how to deal with problems that involve angular measures and how to calculate the exact values of trigonometric functions for any angle using reference angles and then determining its sign, depending on the quadrant.
The reference angle is defined as the acute angle between the terminal side of the given angle and the x axis. The given angle may be in degrees or radians. (More text below video...)
<h2>Trigonometry - Finding reference angles</h2> <p>reference angle, trigonometric functions, video, example, quadrant, terminal side, third quadrant, sine, cosine, tangent, cotangent, sin, cos, tan, cot, sec, csc, solutions, angle, fourth quadrant, formula, exact values, first quadrant, positive, second quadrant, practice question, quizzes</p> <p>The reference angle is defined as the acute angle between the terminal side of the given angle and the x axis.</p>
Other useful lessons:
Trigonometric Functions - Angles
Trigonometric functions of any angle
(Continued from above) The important characteristics are:
  • In the First quadrant:  All the trigonometric function values are positive.
  • In the Second quadrant:  Only sine and cosec functions are positive.
  • In the third quadrant:  Only tangent and cotangent functions are positive.
  • In the fourth quadrant:  Only cosine and secant functions are positive.

The reference angles for different quadrants are as follows:
  • Angle (90 - ) lies in first quadrant
  • Angle (180 - ) lies in second quadrant
  • Angle ( - 180) lies in third quadrant
  • Angle (360 - ) lies in fourth quadrant
For example, the reference angle to angle A = 120 is given by (180 - 120) = 60 and to angle A = 330(that lies in the IV quadrant), the reference angle is (360 - 330) = 30. The value of sin 30 = 1/2, which gives sin 330 = -1/2.
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