Unit 5 – D6 C.A.S.T. Rule
Can you tell what the following all have in common?
sin 35o
sin 145o
sin 215o
sin 325o
Evaluate:
sin 35o
sin 325o
sin 145o
sin 215o
Quadrant II
90o ≤ θ ≤ 180o
Quadrant I
0o ≤ θ ≤ 90o
sinθ =
cosθ =
tanθ =
sinθ =
cosθ =
tanθ =
Quadrant III
180o ≤ θ ≤ 270o
Quadrant IV
180o ≤ θ ≤ 360o
sinθ =
cosθ =
tanθ =
sinθ =
cosθ =
tanθ =
C.A.S.T. Rule
- tells us where each trig ratio is positive
We use the CAST rule to determine the
correct sign of any trig ratio.
Unit 5 – D6 Ex. 1) Use the CAST rule to determine the two angles (nearest tenth) associated with cos θ = -0.627
between 0o ≤ θ ≤ 360o
Steps:
1. Use CAST to determine which
quadrants the terminal arm
could lie in.
2. Draw diagram including labels.
3. Find the RAA - by taking the
inverse of the POSITIVE ratio
value.
4. Use RAA to find both possible
angles of the terminal arm.
Ex. 2) Find the two angles 0o ≤ θ ≤ 360o associated with the following trig ratio.
tan θ = - 0.2679
Ex. 3) If θ is in standard position, with its terminal arm in the specified quadrant and 0o ≤ θ ≤ 360o, find the
exact value of the other two trig ratios and the principal angle.
cos θ = 4 , quadrant IV
7
Practice:
pg. 349 # 6, 7
0o ≤ θ ≤ 360o for all questions