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Reflective Portfolio
Trigonometry
Section #1: Vocabulary (words and/or diagrams)
Define each:
 Acute angle
 Angle in standard position
 Initial side
 Terminal side
 Coterminal angle
 Reference Triangle
 Reference angle
 Radian
 1st degree trig equation
 2nd degree trig equation
 Pythagorean Identities – show deriving from sin 2 x  cos 2 x  1
 Reciprocal Identities
 Quotient Identities
 Sinusoidal Graphs
Amplitude, Frequency, Phase shift, Vertical shift, Period, Midline
Section #2: Formulas/Equations
 Pythagorean Theorem
 Special Right Triangle Ratios (45-45-90, 30-60-90)
opposite
 Six Trig ratios ( sin  
, etc)
hypotenuse
 In which quadrants is each trig function positive?
 Reciprocal Functions
 Cofunctions
 In the unit circle, the cosine is the ____-coordinate, the sine is the _____-coordinate and the
tangent is _____________.
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s  r
(explain and give an example)
Standard form: y  A sin( B( x  C )  D where A = ? ;B =? ;C = ?;D =?
On the reference sheet
o Area of a Triangle– you must use 2 sides and the included angle
o Law of Sines
o Law of Cosines
Section #3: Key methods and concepts (write out the process and include an example)
 How to find the exact value of a trigonometric function
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o Include the following examples: cos 135º, csc 330º, tan
4
12
o Another example to include: if tan    and sin  > 0, find cos .
5
 How to convert radians to degrees
 How to convert degrees to radians
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How to solve a 1st degree trig equation
o Example: Solve for  such that 0    360 : 2 cos  1
How to solve a 2nd degree trig equation
o Example: Solve for  such that 0    360 : cos 2   2 cos   3  0
How to solve a trig equation using identities
o Example: Find all values of θ in the interval 0° ≤ θ < 360° which satisfy the equation
2sinθ − 1 = cscθ
o Example: Find, to the nearest degree, all values of θ in the interval 0° ≤ θ < 360° which
satisfy the equation 2 sin 2   2 cos   1  0 (use quadratic formula)
Solving for Trig functions of non-special angles (not 30, 60, 90, 45, etc)
o To get the exact value, change the angle to a sum or difference of 2 angles, half angle, or
double angle and solve using the identities from the reference sheet.
o Example: Find the value of sin170°cos20° − cos170° sin20°
cos 2 A  sin 2 A
o Example: Express
as a single trig function.
cos A
How to round to the nearest minute
o On calc: 2nd APPS option 4:DMS, enter, enter
If seconds < 30, keep minutes, otherwise round up to next minute
To find the area of a triangle without a known height:
o Example #1: Find the area of a triangle when two sides are 8 in. and 18 in. and the
includes angle is 42°
To find missing sides and angles of non-right triangles, called oblique triangles, use Law of
Sines or Law of Cosines from Reference Sheet
o Example #2: a) Find the measure of angle B to the nearest degree.
b) Ambiguous Case: How many unique triangles?
o Example #3: Find angle C.
o Example #4: Find the length of c
Example
Example
Example
#2
#3
Resultant
Vector - Magnitude
#4
o Example #5: A force of 11 pounds and a force of 6 pounds act on an object at an
angle of 41° with respect to one another. What is the magnitude of the resultant
force, and what angle does the resultant force form with the 11-pound force?
This study guide needs to be NEAT and ORGANIZED!!!
(or you may lose credit)
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Example
#5
Trig Graphs
Sketch the following trig graphs.
y  sin( x)
y  cos(x)
y  tan( x)
y  csc( x)
y  sec(x )
y  cot(x)
y  sin 1 ( x)
y  cos 1 ( x)
y  tan 1 ( x)