Trigonometry Review
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Hopefully, you remember these from last year (you
were required to memorize ten of them) plus SOH
CAH TOA.
If not, you need to know the reciprocal and quotient
identities which are in the blue box on pg A17, and
the Pythagorean, Addition, and Double-Angle
Formulas which are inside the back cover of your
books.
If you need more information, see the Trig Identity
Flash cards information under Chapter 5 of
PreCalculus on my website.
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Please review vocabulary on pg A16 regarding
standard position, initial side, and terminal
side of angles.
Remember (see Figure B.9) that the
coordinates of the point where your terminal
side intersects the unit circle correspond to
sine and cosine. P(x,y): the x coordinate is
the cosine (adjacent/1 hyp) and the y
coordinate is the sine (opposite/1).
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Remember that the first quadrant is where x
and y are both positive and that the
numbering continues counterclockwise.
Also, we learned a pneumonic device to
remember signs (see Fig. B.13 on pg A18).
◦ All Students Take Calculus
 In quadrant I, All signs are positive for sin, cos, tan
and their reciprocals.
 In quadrant II, only Sin (and its reciprocal) is/are pos.
 In quadrant III, only Tan (and its reciprocal) is/are pos.
 In quadrant IV, only Cos (and its reciprocal) is/are pos.
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The law of cosines helps to find an unknown
angle when you are given SSS (side, side,
side) or the unknown side when you are given
SAS and the triangle is not a right triangle.
Law of Cosines:
◦ c² = a² + b² - 2abcosƟ
◦ There is a proof on page A20 if you are interested.
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There are many other Trigonometric
Identities and Formulas in this Appendix and
inside the back cover of your book. You
should be familiar with them and know how
to use them, but you do not need to
memorize them.
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Use the information from slides #3 and #4 to
draw the appropriate triangle(s) in a unit
circle.
Work backwards using special triangles to
determine the appropriate angle.
See example 6 on pages A22&A23.
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If Ɵ is the smallest angle measured
counterclockwise from the x-axis, then the
slope of the line is the same as the tan Ɵ.
◦ m= tan Ɵ
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This makes sense because m = rise/run and
tan Ɵ = (sin Ɵ)/(cos Ɵ), the rise is the
opposite side (y=sin Ɵ) and the run is the
adjacent side (x=cos Ɵ).
See figures B.19 & B.20 on pg. A23.