E6 CAST Rule Lesson.notebook
April 21, 2015
Warm up Find the sinθ, cosθ, tanθ and principal angle θ given the point P is on the terminal arm of an angle θ in standard position given P(­2, ­3)
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 145o
sin 215o
sin 325o
How do we know when the value will be positive or negative?
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E6 CAST Rule Lesson.notebook
April 21, 2015
C.A.S.T. Rule
Quadrant II
90o ≤ θ ≤ 180o
Quadrant I
0o ≤ θ ≤ 90o
sinθ = cosθ =
tanθ =
sinθ = cosθ =
tanθ =
Quadrant III
180o ≤ θ ≤ 270o
Quadrant IV
270o ≤ 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.
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E6 CAST Rule Lesson.notebook
April 21, 2015
Ex. 1) Use the CAST rule to determine the two angles 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) Given 0o ≤ θ ≤ 360o calculate tan θ = ­ 0.2679
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.
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E6 CAST Rule Lesson.notebook
April 21, 2015
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
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Work
or Pg. 349 #6,7 4