Home » Trigonometry Quick Review

• Degree - unit of angle measurement equal to 1/360 of a circle’s circumference.
  
• Radian - unit of angle measurement that is the ratio ofthe circle arc cut off by an angle to the central angle.
  
• Sine - on a unit circle, the “y” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
  
• Cosine - on a unit circle, the “x” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.
  
• Tangent - the ratio of sine to cosine or, in a right triangle, the ratio of the length of the opposite side to the length of the adjacent side.
  
• Secant - reciprocal of cosine (sec θ = 1 / cos θ).
  
• Cosecant - reciprocal of sine (csc θ = 1 / sin θ).
  
• Cotangent - reciprocal of tangent (cot θ = 1 / tan θ).
  
• General Form of a Trig Function - trig functions take the form y = A f(Bx + C) + D where A, B, C, and D are coefficients that change the characteristics of that trig function.

Common Angles in Both Degrees and Radians

• Converting Between Degrees and Radians – Set up a ratio using the fact that 180° = ∏ radians: 
  Convert 20° to radians:

Definition for a right triangle
(o=opposite side, a = adjacent side, h = hypotenuse)

• Though sine and cosine are related to the unit circle, their practical value comes from being able to solve right triangles:
• Example:  Given a 40˚ angle and a hypotenuse of 14, find both legs of the right triangle.The proper equation for sine in this case is:
  sin 40˚ = a / 14, so
  14 sin 40˚ = a
  and 9.0 = a
  The proper equation for cosine in this case is:
  cos 40˚ = b / 14, so
  14 cos 40˚ = b
  and 10.7 = b
• Example:  Leg a is 5 and leg b is 8.  What is the angle that is adjacent to leg b and the hypotenuse?
  The proper equation for tan in this case is:
  tan θ  = 5 / 8, so
  tan θ  = 0.625
  using a table or calculator, we take
  the inverse of tangent:
  θ = 32˚

Common Trig Function Values to be Memorized

• When graphing a trig function either:
  Memorize the graph, domain, range and any asymptotes
  or
  reason out major features of each graph and sketch it accordingly. 

Example of finding a basic graph through reasoning:

• We know:
  
  • sin 0° = 0
    
  • sin 90° = sin π/2 = 1
    
  • sin 180° = sin π = 0
    
  • sin 270° = sin 3π/2 = -1
    
  • sin 360° = sin 2π = 0
• Additionally:
  
  • sin π/6 = 1/2
    
  • sin π/3 = √3/2 = 0.866

 

• Important traits for y = sin x: 
  • Domain: All real nos.
  • Range: [-1, 1]
  • Repeats every 2π over the entire x axis