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UNIT
7 : TRIGONOMETRIC FUNCTIONS
LESSON 2:
ANGLES IN STANDARD POSITION
Angles in Standard Position:
Definition: An angle is in standard position
if it has its vertex at the origin and initial arm along the positive
x-axis. The terminal arm is found by
rotating
the initial
arm about the origin to a terminal position in one of the 4 quadrants. The rotation is positive if it is in the
counter – clockwise direction and negative
if in the
clockwise direction.
.
Note that
all three ratios are positive for a first quadrant angle.
Note
that sine is positive and cosine and tangent are negative for a second quadrant
angle.
Note
that tan is positive and sine and cosine are negative for a third quadrant
angle.
Note
that cos is positive and sine and tangent are
negative for a fourth quadrant angle.
The CAST rule:
The
CAST
RULE is a memory aid which tells us the sign of the trig ratios
in the various quadrants.
In the first quadrant ALL are
positive. This is denoted using the
letter A.
In the second quadrant, SINE is
positive. This is denoted by the letter S.
[ the
other two ratios are negative ]
In the third quadrant, TANGENT is
positive. This is denoted by the letter T.
[ the
other two ratios are negative ]
In the fourth quadrant, COSINE is
positive. This is denoted by the letter C.
[ the
other two ratios are negative ].
Special Triangles:
These triangles enable us to find the trig ratios of
acute angles 300, 450 , 600
and their related angles
Trig. Ratios of any Angles in Standard
Position:
