Basic trigonometry II | Basic trigonometry | Trigonometry | Khan Academy

TL;DR

Learn how to find the trigonometric functions (sine, cosine, tangent) in right triangles using the mnemonic "soh cah toa".

Transcript

Let's just do a ton of more examples, just so we make sure that we're getting this trig function thing down well. So let's construct ourselves some right triangles. Let's construct ourselves some right triangles, and I want to be very clear. The way I've defined it so far, this will only work in right triangles. So if you're trying to find the trig... Read More

Key Insights

• 🗯️ Trigonometric functions in right triangles can be found using the Pythagorean theorem.
• 🥳 The "soh cah toa" mnemonic helps remember the trigonometric functions (sine, cosine, tangent) and their corresponding ratios.
• ✖️ Rationalizing the trigonometric functions can be done by multiplying the numerator and denominator by the conjugate of the denominator.

Questions & Answers

Q: What is the relationship between the lengths of the sides in a right triangle?

In a right triangle, the lengths of the sides are related by the Pythagorean theorem, where the hypotenuse squared is equal to the sum of the squares of the other two sides.

Q: How can the trigonometric functions be determined in a right triangle?

By using the mnemonic "soh cah toa," the sine, cosine, and tangent of an angle in a right triangle can be determined based on the lengths of the sides.

Q: How can the trigonometric functions be rationalized?

To rationalize the trigonometric functions, the numerator and denominator can be multiplied by the conjugate of the denominator to eliminate irrational numbers in the denominator.

Q: What is the relationship between the trigonometric functions for different angles in a right triangle?

The trigonometric functions for complementary angles (30 and 60 degrees) have a reciprocal relationship, where the sine of 30 degrees is equal to the cosine of 60 degrees, and vice versa.

Summary & Key Takeaways

• Trigonometric functions can be found in right triangles using the Pythagorean theorem.

• The "soh cah toa" mnemonic helps remember which trigonometric function to use.

• The trigonometric functions (sine, cosine, tangent) can be determined based on the sides of the right triangle.