MCR 3U – Unit 5: Trigonometry
Date: __________________
Trigonometry of Any Angle – The CAST Rule
Recall:
To work with angles greater than 90 , we formed a right-triangle using the terminal arm and the related
acute angle. (Lesson 5)
The CAST Rule
Any angle in standard position has a related acute angle. An acute right-triangle can always be drawn
using this RAA, thus any angle can be associated with the primary trig ratios.
The quadrant will determine the sign (+ or -) of the ratio.
Page 1 of 6.
Ex. 1: Consider the Point (4,3)
Ex. 2: Consider the Point (-4, 3)
Page 2 of 6.
Ex. 3: Consider the Point (-4, -3)
Ex. 4: Consider the Point (4, -3)
The CAST rule allows us to quickly determine the sign of each trig ratio for any quadrant.
Ex. 5: Predict the sign (+ or -) of each value. (Verify using your calculator)
a) tan 135
b) cos 240
c) sin 430
d) tan( 30)
Page 4 of 6.
a) Where (in which quadrant) is  located?
b) Determine the Primary Trig Ratios.
c) Determine the value of  to the nearest degree.
Assigned Work: pg. 281 #3(a-h) where
Page 6 of 6.