Questions: Match each trig function with its ratio. © Tangent © Sine a. (adj)/(hyp) - Cosine b. (opp)/(adj) c. (adj)/(opp) d. (hyp)/(opp) e. (opp)/(hyp) f. (hyp)/(adj)

Match each trig function with its ratio. © Tangent © Sine a. (adj)/(hyp) - Cosine b. (opp)/(adj) c. (adj)/(opp) d. (hyp)/(opp) e. (opp)/(hyp) f. (hyp)/(adj)
Transcript text: Match each trig function with its ratio. © Tangent © Sine a. $\frac{a d j}{h y p}$ - Cosine b. $\frac{o p p}{a d j}$ c. $\frac{a d j}{o p p}$ d. $\frac{h y p}{o p p}$ e. $\frac{o p p}{h y p}$ f. $\frac{h y p}{a d j}$
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Solution

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Solution Steps

Step 1: Identify the trigonometric functions and their ratios

The trigonometric functions mentioned are:

  • Tangent
  • Sine
  • Cosine

The ratios provided are:

  • a. \(\frac{adj}{hyp}\)
  • b. \(\frac{opp}{adj}\)
  • c. \(\frac{adj}{opp}\)
  • d. \(\frac{hyp}{opp}\)
  • e. \(\frac{opp}{hyp}\)
  • f. \(\frac{hyp}{adj}\)
Step 2: Match each trigonometric function with its correct ratio
  • Tangent: The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Therefore, Tangent corresponds to \(\frac{opp}{adj}\), which is option b.
  • Sine: The sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse. Therefore, Sine corresponds to \(\frac{opp}{hyp}\), which is option e.
  • Cosine: The cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. Therefore, Cosine corresponds to \(\frac{adj}{hyp}\), which is option a.

Final Answer

  • Tangent: \(\boxed{b}\)
  • Sine: \(\boxed{e}\)
  • Cosine: \(\boxed{a}\)
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