Recall: To work with angles greater than 90°, we form a
right­triangle using the terminal arm and the related
acute angle.
For any angle of interest (θ), there are three (3) primary trigonometric ratios.
se
opposite
to θ
sine of θ= opposite
hypotenuse
adjacent
cosine of θ=
hypotenuse
opposite
tangent of θ=
adjacent
nu
te
po
hy
2nd
quadrant
(obtuse angle)
90°
1st
quadrant
(acute angle)
θ
adjacent to θ
S o h C a h T o a
180°
RAA
θ
0°, 360°
4th
quadrant
3rd
quadrant
270°
Apr 25­9:54 PM
Apr 19­9:19 PM
y
Trigonometry of Any Angle:
The CAST Rule
y
(a, b)
(­a, b)
r
r
y = b
y = b
180°−θ
θ
x
x
x = a
x = ­a
Any angle in standard position has a related acute angle.
An acute right­triangle can always be drawn using this
RAA, thus any angle can be associated with the
primary trig ratios.
The quadrant will determine the sign of the ratio.
or
Apr 25­10:27 PM
Apr 19­9:13 PM
Ex.1 Consider P(4, 3)
Apr 19­9:13 PM
Ex.2 Consider P(­4, 3)
Apr 19­9:13 PM
Ex.3 Consider P(­4, ­3)
Ex.4 Consider P(4, ­3)
Apr 19­9:13 PM
Apr 19­9:13 PM
The CAST rule allows us to quickly determine the
sign of each trig ratio for any quadrant.
sin +
cos ­
tan ­
sin +
cos +
tan +
sin ­
cos ­
tan +
sin ­
cos +
tan ­
S
A
T
C
Ex.5 Predict the sign of each value (verify with calculator)
(a) tan 135°
(c) sin 430°
May 3­9:19 AM
(b) cos 240°
(d) tan(­30°)
May 3­9:22 AM
Ex.6 For
Ex.6 For
(a) where (which quadrant) is θ?
(c) determine the value of θ to the nearest degree
(b) determine the primary trig ratios
May 3­9:24 AM
May 3­9:24 AM
Assigned Work:
TBD
Apr 21­12:17 AM