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Topic
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5.5 SPECIAL ANGLES |
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Team members |
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HASEEB SHARIFI
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Overview |
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This chapter is all about special angles.
Special angles are angles in trigonometry which
have exact values. Exact values are determined
by geometric relationships. Special angles only
work with right isosceles or equilateral
triangles. The angels in the isosceles triangles
are 45, 45, 90 degrees. In equilateral triangles
the angles are 60, 30, 90 degree. Being able to
draw an angle in standard position, you can
determine the sine, cosine and tangent of the
angle without using a calculator. You can expect
being given an angle and having to draw it in
standard position, label the sides and figure
out the sine, cosine and the tangent of the
angles in exact values.
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Study Tips,
Methods and or Advice |
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In Standard
Position
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Sin |
0 |
1 |
0 |
-1 |
0 |
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Cos |
1 |
0 |
-1 |
0 |
1 |
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Tan |
0 |
Und |
0 |
Und |
0 |
MEMOREIZE THIS CHART OF
SPECIAL CASE ANGLES
Remember These Special
Triangles Remember the
CAST rule
Remember: SOH CAH TOA
For
Triangles
= =
Sin=
Cos=
Tan =
For
Triangles
=
=
Tan =
EXAMPLE
Determine the exact values
for Sin,
Cos and
Tan
TIPS IN SOLVING THE
EQUATION
1) Draw angle in standard
position
2) Sketch a right angle
triangle
3) Label side lengths of
triangle
1)
2) 
=
=
=
=
=
=
-1
* The Golden Rule in order
to have success in this chapter is to DO ALL OF
YOUR HOMEWORK.
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Questions |
Complete Solutions |
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1.
Determine the exact
values for Sin,
Cos and
Tan
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=
Cos =
Tan =
=
=
=
1
=
,
=
,
=
1
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2.
Determine the exact
values for Sin,
Cos and
Tan
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=
Cos =
Tan =
= -
=
=
=
- ,
=
,
=
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3.
Determine the exact
values for Sin,
Cos and
Tan
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=
Cos =
Tan =
= =
-
=
=
,
=
-,
=
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4.
Determine the exact
values for Sin,
Cos and
Tan
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=
Cos =
Tan =
= -
=
=
-1
=
-
,
=
,
=
-1
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Extra
Practice Questions and Answers |
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Extra Practice Questions |
Answers |
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1.
Determine the exact
values for Sin,
Cos and
Tan
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=
=
=
1
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2.
Determine the exact
values for Sin,
Cos and
Tan
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=
=
=
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3.
Determine the exact
values for Sin,
Cos and
Tan
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=
=
=
-1 |
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4.
Determine the exact
values for Sin,
Cos and
Tan
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=
=
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