UNIT 1 

What's an Angle?

                 Angles: 
An angle is drawn in standard position where the vertex is at the origin and one side is fixed on the x axis. 

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Angles and its Inverse

To find the angle of a right triangle you have to use inverse.  Inverse always finds angle. 
Example:  
      Suppose x is 10 and y is 15, then 
      tan= 10/15=2/3=0.67
     Find inverse of tan use tan-1 
           = 33 degrees

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Degrees and Radians 

• Radian measure is just a different way of talking about the circle. Radian measure is just different unit of measure.  
  
• When converting degrees to radians you simply multiply the number of degree by pie/180 degrees 
  

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Degrees to Radians
Example 1
Convert 200° into radian measure: 
200∘⋅π180∘=10π9 radians =3.49 radians 
Explanation: You multiply across and then simplify to get your answer 3.49.
Example 2
Convert 120° into radian measure:
120∘⋅π180=2π3 radians =2.09 radians
 

Radians to Degrees 
Example 1
Convert 49π radians to degrees 4π9⋅180∘π=4π⋅180∘⋅9π=
720∘π⋅9π720∘π⋅9π
      =80∘
Explanation: You want to cancel out the pie and if you could reduce then you reduce 180 and 9 and you simplify at the end. 
Example 2
Convert 1.4 radians into degrees:
1.4⋅180∘π=252∘π≈80.2∘

                    Sine                                                                      

Sine= y

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Cosine

     Cosine=x 

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• Opposite is always opposite from the given angle or the angle the problem is asking for
  
• Adjacent is next to the angle
  
• Hypotenuse s the longest side and is always across the 90 degree angle

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Their definition as x- & y-coordinates on the unit circle: The Unit Circle is composed of points for example (1/2, square root of 3/2) x would be 1/2 and y is square root of 3/2. Where X is Cosine and Y Sine. 

Finding Missing Angles and Sides: Students are capable of computing unknown sides or angles in a right triangle.

So we are focusing on angle A which is 36 degrees. To find a we use Sin which is opp/hyp. Hypotenuse is always across the right angle. 
      sine36= a/10       Multiply by 10 to get a by its self        
                10sin36=a  Put it into the Calculator 
                                                               a=8.5                        

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Word Problem 

A 95-ft tree casts a shadow that is 45 ft long. What is the angle of elevation of the sun?
Step 1: Draw the triangle and label the given parts. Look for key words that help you determine what angle you are looking for. In this example the word is Elevation.
Step 2: Use basic trigonometric functions. In this example I would use tan which is opp/hyp.
                                      TanX= 95/45
Step 3: Use the inverse property to find the angle
                                        TanX= (95/45)tan-1
Step 4:  tanx= 65 degrees

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Unit 2 

Functions of the form f(t)=A sin (Bt + C) & f(t)=A cos (Bt + C):

• Graphing
• Properties: amplitude, frequency, period and phase shift (A, B & C)
• Student will be able to take a given angle and compute the trigonometric function and its inverse with the aid of the unit circle (by hand)
• Students use trigonometry in a variety of word problems.
  

4.4, 4.5, 4.7, 4.8

Unit 3:

 Analytical Trigonometry:

• Fundamental Identities
• Sum and Difference Formulas
• Use double-angle and half-angle formulas to prove and/or simplify other trigonometric identities.

         5.1, 5.2, 5.3, 5.4

Analytical Trigonometry:

• Students will be familiar with the law of sines and law of cosines to solve problems

5.5, 5.6

Unit 4: 

Applications of Trigonometry:

• Students need to know how to write equations in rectangular coordinates in terms of polar coordinates.
• Vectors
• Parametric Relations

6.1, 6.2, 6.3, 6.4, 6.5