This math topic focuses on identifying trigonometric relationships involving sine, cosine, and tangent from given fact families. It covers the fundamental properties of ratios of sides in right-angled triangles (opposite, adjacent, hypotenuse) and their application in formulating correct trigonometric expressions. The problems require understanding and selecting the correct trigonometric formulas that represent the relationships discussed. These exercises serve as an introduction to trigonometry fundamentals, enhancing students' ability to decode and use trigonometric identities effectively.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Fact Family - Sin/Cos/Tan - Triangle to Fact Worksheet

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Fact Family - Sin/Cos/Tan - Triangle to Fact
1
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{hyp} = \frac{\text{opp}}{\text{sin}}
b A LaTex expression showing \text{hyp} = \frac{\text{sin}}{\text{opp}}
c A LaTex expression showing \text{opp} = \frac{\text{hyp}}{\text{sin}}
2
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{adj} = \frac{\text{cos}}{\text{hyp}}
b A LaTex expression showing \text{cos} = \frac{\text{hyp}}{\text{adj}}
c A LaTex expression showing \text{cos} = \frac{\text{adj}}{\text{hyp}}
3
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{adj} times \text{tan} = \text{opp}
b A LaTex expression showing \text{adj} times \text{opp} = \text{tan}
c A LaTex expression showing \text{opp} times \text{tan} = \text{adj}
4
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{adj} = \frac{\text{tan}}{\text{opp}}
b A LaTex expression showing \text{opp} = \frac{\text{adj}}{\text{tan}}
c A LaTex expression showing \text{adj} = \frac{\text{opp}}{\text{tan}}
5
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{hyp} times \text{opp} = \text{sin}
b A LaTex expression showing \text{opp} times \text{sin} = \text{hyp}
c A LaTex expression showing \text{hyp} times \text{sin} = \text{opp}
6
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{cos} = \frac{\text{hyp}}{\text{adj}}
b A LaTex expression showing \text{cos} = \frac{\text{adj}}{\text{hyp}}
c A LaTex expression showing \text{adj} = \frac{\text{cos}}{\text{hyp}}
7
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{adj} times \text{hyp} = \text{cos}
b A LaTex expression showing \text{cos} times \text{hyp} = \text{adj}
c A LaTex expression showing \text{cos} times \text{adj} = \text{hyp}
8
Which trigonometry fact comes from this fact family
An svg image showing a math problem
a A LaTex expression showing \text{cos} = \frac{\text{hyp}}{\text{adj}}
b A LaTex expression showing \text{cos} = \frac{\text{adj}}{\text{hyp}}
c A LaTex expression showing \text{adj} = \frac{\text{cos}}{\text{hyp}}