Trig identities part 2 (part 4 if you watch the proofs) | Trigonometry | Khan Academy

TL;DR

A review of trigonometry basics, including trig identities and their relationships, with examples and derivations.

Transcript

Welcome back. I'm now going to do a bit of a review of everything we've learned so far about maybe even trigonometry and trig identities. And then we'll see if we can come up with-- maybe use what we already know to come up with a couple more trig identities. So we know that from SOH-CAH-TOA we know that sine of theta is equal to the opposite over ... Read More

Key Insights

• 🔺 Trigonometry involves the study of relationships between angles and sides of triangles.
• 🙃 Trigonometric functions such as sine, cosine, and tangent are defined based on ratios of sides in right triangles.
• 👻 Trig identities, such as reciprocals and Pythagorean identities, allow for simplification and manipulation of trigonometric equations.

Questions & Answers

Q: What are the basic trigonometric functions and how are they defined?

The basic trigonometric functions are sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse in a right triangle, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

Q: What are the reciprocals of the basic trigonometric functions?

The reciprocals of the basic trigonometric functions are cosecant, secant, and cotangent. Cosecant is the reciprocal of the sine function (1/sine), secant is the reciprocal of the cosine function (1/cosine), and cotangent is the reciprocal of the tangent function (1/tangent).

Q: How are trigonometric identities derived from basic trigonometric functions?

Trigonometric identities can be derived by manipulating and combining the basic trigonometric functions. For example, the identity sine squared plus cosine squared equals one can be derived using the Pythagorean theorem, where the squared lengths of the opposite and adjacent sides of a right triangle are added together and equal the squared length of the hypotenuse.

Q: What is the relationship between sine, cosine, and tangent?

The relationship between sine, cosine, and tangent is that tangent is equal to sine divided by cosine. This relationship can be derived from the definitions of sine and cosine and is often used to simplify calculations involving trigonometric functions.

Summary & Key Takeaways

• The content provides a review of basic trigonometry concepts, including SOH-CAH-TOA, trigonometric functions, and their inverses.

• Trig identities such as sine squared plus cosine squared equals one and tangent squared plus one equals secant squared are discussed.

• The video demonstrates how trig identities can be used to derive new identities and explores the relationships between sine, cosine, and tangent.