U4A L1 CAST Rule and Unit Circle Skill Builder
Completion requirements
Unit 4A
Trigonometry Part 1
Lesson 1: Trigonometry Review
Skill Builder
CAST Rule
CAST is an acronym you can use to remember in which quadrant each of the trigonometric ratios is positive. Write the letters in C-A-S-T in each quadrant, starting from Quadrant IV and rotating counter-clockwise. The letter in each quadrant represents
the ratio that is positive, while the other ratios are negative.
- C means only cosine is positive in Quadrant IV
- A means all ratios are positive in Quadrant I
- S means only sine is positive in Quadrant II
- T means only tangent is positive in Quadrant III
Given the standard position angle of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»145«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math», determine which trigonometric ratio is positive.
Because «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»145«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math» is less than «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»180«/mn»«mo»§#176;«/mo»«/mstyle»«/math» and more than «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»90«/mn»«mo»§#176;«/mo»«/mstyle»«/math», it terminates in Quadrant II.
In Quadrant II, only sine is positive (the "S" in CAST). As such, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»sin«/mi»«mn»145«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math» is positive.
Step 1:
Determine in which quadrant the angle terminates.
Because «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»145«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math» is less than «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»180«/mn»«mo»§#176;«/mo»«/mstyle»«/math» and more than «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»90«/mn»«mo»§#176;«/mo»«/mstyle»«/math», it terminates in Quadrant II.
Step 2:
Using CAST, determine which ratio is positive.
In Quadrant II, only sine is positive (the "S" in CAST). As such, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»sin«/mi»«mn»145«/mn»«mo»§#176;«/mo»«/mrow»«/mstyle»«/math» is positive.