Matching ratios to trig functions | Trigonometry | Khan Academy

TL;DR

This video explains the process of determining the equivalent trigonometric expressions based on the unit circle definition and the soh cah toa definition.

Transcript

Voiceover:On the right-hand side we have a bunch of expressions that are just ratios of different information given in these two diagrams. Then over here on the left we have the sine taken of angle MKJ, cosine of angle MKJ, and tangent of angle MKJ. Angle MKJ is this angle right over here same thing as theta, so these two angles. These two angles h... Read More

Key Insights

• 😑 Trigonometric expressions can be determined using the unit circle definition or the soh cah toa definition.
• ⭕ The unit circle definition connects the cosine and sine of an angle to the X and Y coordinates on the unit circle, respectively.
• 😑 Reciprocal trigonometric functions, such as the reciprocal of tangent or cosine, can help determine the equivalence of certain expressions.

Questions & Answers

Q: How is the unit circle definition related to the soh cah toa definition of trigonometric functions?

The unit circle definition is an extension of the soh cah toa definition. It connects the X and Y coordinates of where a ray intersects the unit circle to the cosine and sine of an angle, respectively.

Q: How can we determine which trigonometric expression is equivalent to X over one?

X over one is equal to the adjacent side over the hypotenuse, which is the definition of cosine. Therefore, X over one is equivalent to the cosine of the angle.

Q: What is the reciprocal of the tangent function and why is it relevant in this analysis?

The reciprocal of tangent is one over tangent, which is equal to adjacent over opposite. In this analysis, it is used to determine the equivalence of certain trigonometric expressions.

Q: How can we decide which trigonometric expression is equivalent to M over J?

M over J represents the hypotenuse over the adjacent side, which is the reciprocal of cosine. Therefore, M over J is equivalent to one over the cosine of the angle.

Summary & Key Takeaways

• The video discusses trigonometric expressions and their equivalents, using the unit circle and soh cah toa definitions.

• It explains how to identify the adjacent and opposite sides of a right triangle and relate them to the cosine, sine, and tangent of an angle.

• The video also explores the reciprocal trigonometric functions and their relationships with the original trigonometric functions.