L1 Trigonometry Review - Part 2
Completion requirements
Unit 4A
Trigonometry Part 1
Lesson 1: Trigonometry Review
Primary and Reciprocal Trigonometric Ratios
Recall, from previous math courses, the three primary trigonometric ratios are sine, cosine, and tangent.Given the acute angle «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo»§#952;«/mo»«/mstyle»«/math», the three primary trigonometric ratios for the right triangle «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»A«/mi»«mi»B«/mi»«mi»C«/mi»«/mrow»«/mstyle»«/math» are as follows.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable columnalign=¨right center left¨»«mtr»«mtd»«mi»sin«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»opposite«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»opp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»hypotenuse«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»hyp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»a«/mi»«mi»c«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»cos«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»adjacent«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»adj«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»hypotenuse«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»hyp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»b«/mi»«mi»c«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»tan«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»opposite«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»opp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»adjacent«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»adj«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»a«/mi»«mi»b«/mi»«/mfrac»«/mtd»«/mtr»«/mtable»«/mstyle»«/math»
| Use the acronym SOH-CAH-TOA to help remember the ratios.
Sine is Opposite over Hypotenuse Cosine is Adjacent over Hypotenuse Tangent is Opposite over Adjacent |
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable columnalign=¨right center left¨»«mtr»«mtd»«mi»csc«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mrow»«mi»sin«/mi»«mo»§#952;«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»hypotenuse«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»hyp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»opposite«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»opp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»c«/mi»«mi»a«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»sec«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mrow»«mi»cos«/mi»«mo»§#952;«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»hypotenuse«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»hyp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»adjacent«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»adj«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»c«/mi»«mi»b«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»cot«/mi»«mo»§#952;«/mo»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mrow»«mi»tan«/mi»«mo»§#952;«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»adjacent«/mi»«mi
mathvariant=¨normal¨»(«/mi»«mi»adj«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«mrow»«mi»opposite«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»opp«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»b«/mi»«mi»a«/mi»«/mfrac»«/mtd»«/mtr»«/mtable»«/mstyle»«/math»
Determine the primary trigonometric ratios for the right triangle shown.
Notice the answers are left as fractions rather than decimals. When answers are left in fraction form, and not decimal form, the solution is referred to as an exact value.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable»«mtr»«mtd»«mi»sin«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»5«/mn»«mn»13«/mn»«/mfrac»«/mtd»«mtd/»«mtd/»«mtd»«mi»cos«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»12«/mn»«mn»13«/mn»«/mfrac»«/mtd»«mtd/»«mtd/»«mtd»«mi»tan«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»5«/mn»«mn»12«/mn»«/mfrac»«/mtd»«/mtr»«/mtable»«/mstyle»«/math»
Notice the answers are left as fractions rather than decimals. When answers are left in fraction form, and not decimal form, the solution is referred to as an exact value.
Determine the reciprocal trigonometric ratios, as exact values, for the right triangle shown.
«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mtable»«mtr»«mtd»«mi»csc«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»13«/mn»«mn»5«/mn»«/mfrac»«/mtd»«mtd/»«mtd/»«mtd»«mi»sec«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»13«/mn»«mn»12«/mn»«/mfrac»«/mtd»«mtd/»«mtd/»«mtd»«mi»cot«/mi»«mo»§#952;«/mo»«mo»=«/mo»«mfrac»«mn»12«/mn»«mn»5«/mn»«/mfrac»«/mtd»«/mtr»«/mtable»«/mstyle»«/math»