U2 D2 CAST Rule and Special Triangles Continued Lesson.notebook
February 19, 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
The cast rule gives you another way to determine where the primary trig ratios will be positive or negative without having to consider the signs of x, y, and r.
Determine which ratios will be positive in each quadrant by choosing an angle measure that falls within the given values and calculating the sine, cosine, and tangent of the angle.
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 =
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U2 D2 CAST Rule and Special Triangles Continued Lesson.notebook
February 19, 2015
SUMMARY of 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.
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.
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U2 D2 CAST Rule and Special Triangles Continued Lesson.notebook
February 19, 2015
Ex. 2) 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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Recall from last week:
Special Triangle #1
What else do we know about this triangle?
1
sin 45 = 1
cos 45 = Angles ­ Sides ­
tan 45 =
Special Triangle #2
Angles ­ Sides ­
sin 30 = sin 60 = cos 30 = cos 60 = tan 30 =
tan 60 =
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U2 D2 CAST Rule and Special Triangles Continued Lesson.notebook
February 19, 2015
Ex. 3) If 0o ≤ θ ≤ 360o, Calculate the possible measures of angle θ.
a) sinθ = ­1
√2
b) tanθ = ­√3
Ex. 4) Find the exact value of tan 330o cos 135o
Work: handout
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