In trigonometry, special angles have exact trigonometric values, which are useful for simplifying calculations and solving problems. The special angles are 30°, 45°, and 60°.

30°/60°Angle

Reference Triangle: The 30° angle is often found in a 30°-60° triangle, which is half of an equilateral triangle.

45° Angle

Reference Triangle: The 45° angle is found in a 45° triangle, which is an isosceles right triangle.

• In a 45° triangle, both legs are equal in length.

Use this concept whenever you get a reference angle of 30,60 or 45. make sure to draw the triangles and refer to them throughout the question. use the x,y and r values given by the triangles.

Problem: Find the exact values of sin⁡(150°), cos⁡(210°), and tan⁡(330°)

$sin\; (150°)$

1. Reference Angle: 180°−150°=30
2. Trigonometric Value: sin 30° = y/r —> square root of 3/2 

$\cos (210°)$

1. Reference Angle: 210°−180°=30 
2. Trigonometric value: cos 30°= x/r —> 1/2

$\tan (330°)$

1. Reference Angle: 360°−330°=30°
2. Trigonometric Value: tan⁡(30°)= y/x —-> 2