The reciprocal trigonometric ratios

Trigonometric ratios review

Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant.

What are the trigonometric ratios?

sin⁡(∠A)=\large\sin(\angle A)=oppositehypotenuse\large\dfrac{\blueD{\text{opposite}}}{\goldD{\text{hypotenuse}}}
cos⁡(∠A)=\large\cos(\angle A)=adjacenthypotenuse\large\dfrac{\purpleC{\text{adjacent}}}{\goldD{\text{hypotenuse}}}
tan⁡(∠A)=\large\tan(\angle A)=oppositeadjacent\large\dfrac{\blueD{\text{opposite}}}{\purpleC{\text{adjacent}}}
cot⁡(∠A)=\large\cot(\angle A)=adjacentopposite\large\dfrac{\purpleC{\text{adjacent}}}{\blueD{\text{opposite}}}
sec⁡(∠A)=\large\sec(\angle A)=hypotenuseadjacent\large\dfrac{\goldD{\text{hypotenuse}}}{\purpleC{\text{adjacent}}}
csc⁡(∠A)=\large\csc(\angle A)=hypotenuseopposite\large\dfrac{\goldD{\text{hypotenuse}}}{\blueD{\text{opposite}}}
Want to learn more about sine, cosine, and tangent? Check out this video.
Want to learn more about cotangent, secant, and cosecant? Check out this article.

Practice set 1: sine, cosine, and tangent

Problem 1.1
sin⁡(∠B)=\sin(\angle B)=
  • Your answer should be
  • a proper fraction, like 1/21/2 or 6/106/10
  • a simplified proper fraction, like 3/53/5
  • an improper fraction, like 10/710/7 or 14/814/8
  • a simplified improper fraction, like 7/47/4
Use an exact expression.

Explain
Want to try more problems like this? Check out this exercise.

Practice set 2: cotangent, secant, and cosecant

Problem 2.1
cot⁡(∠B)=\cot(\angle B)=
  • Your answer should be
  • a proper fraction, like 1/21/2 or 6/106/10
  • an improper fraction, like 10/710/7 or 14/814/8
Use an exact expression.

Explain
Want to try more problems like this? Check out this exercise.
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