The CAST Rule
1. For each of the following:
a) sketch and label the angle.
b) indicate the related acute angle (RAA).
i) 40°
ii) 140°
y
iii) 220°
y
y
x
iv) 320°
y
x
x
x
Similarities: ________________________________________________________
Differences: ________________________________________________________
2. Complete the chart below, stating trig ratios accurate to four decimal places.
θ
Quadrant
sinθ
cosθ
tanθ
40°
140°
220°
320°
3. What do you notice about the numbers in the sinθ column? ______________________
4. What do you notice about the numbers in the cosθ column? ______________________
5. What do you notice about the numbers in the tanθ column? ______________________
6. In each of the trig ratio columns, what do you notice about the SIGNS? ____________
__________________________________________________________________
7. Sketch a standard position angle θ in each of the quadrants. On the lines below, each
diagram, record the SIGN of x, y and r.
quadrant I
quadrant II
quadrant III
quadrant IV
y
y
x
y
x
y
x
x
x is ____
x is ____
x is ____
x is ____
y is ____
y is ____
y is ____
y is ____
r is ____
r is ____
r is ____
r is ____
8. Complete the following chart – remember SYR CXR TYX
Quadrant
sign of x
sign of y
sign of r
sign of sinθ
sign of cosθ
sign of tanθ
I
II
III
IV
9. Complete the following chart using the above information.
Quadrant
Which trig ratios are positive?
Which trig ratios are negative?
I
II
III
IV
10. Using the axes provided, complete a SIGN summary for each quadrant.
Simplify the summary:
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_____________________________________________________________________
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4
and θ is an angle in standard position in quadrant II, determine tan θ .
5
Include a clearly labelled sketch.
11. If sin θ =
12. If cos θ =
−2
, 0° ≤ θ ≤ 360°, determine all possible values for sin θ .
5
13. If tan θ =
1
, 0° ≤ θ ≤ 360°, determine all possible values for cos θ .
4