Trigonometric Ratios

TL;DR

Learn how to calculate sine, cosine, and tangent of angles in a right triangle using the SOHCAHTOA method.

Transcript

so this video is about trigonometric ratios let's say if we have a right triangle triangle abc let's say that a b is eight units long bc is 15 and ac is 17 units long what is the value of sine of a that is sine of angle a now you need to be familiar with something called sohcahtoa so this part so tells us that sine of some angle let's say theta is ... Read More

Key Insights

• 🙃 Trigonometric ratios (sine, cosine, tangent) can be found in a right triangle using the lengths of its sides.
• 🥳 The SOHCAHTOA method provides a helpful mnemonic for remembering the trigonometric ratios.
• 🔺 Special right triangles (30-60-90 and 45-45-90) can be used to quickly determine the values of trigonometric ratios for specific angles.
• 🗯️ The Pythagorean theorem can be used to find missing side lengths in a right triangle.
• 🔺 Inverse trigonometric functions can be used to find the measure of an angle in a right triangle.
• 🔺 As the angles in a right triangle approach 90 degrees, the tangent approaches infinity.

Questions & Answers

Q: How do you calculate the sine, cosine, and tangent of an angle in a right triangle?

Using the SOHCAHTOA method, the sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent.

Q: What are the values of sine, cosine, and tangent for angles in special right triangles?

In a 30-60-90 triangle, sine 30 is 1/2, cosine 30 is √3/2, and tangent 30 is 1/√3 (or √3/3 after rationalization). In a 45-45-90 triangle, sine 45 is 1/√2 (or √2/2 after rationalization), cosine 45 is 1/√2 (or √2/2 after rationalization), and tangent 45 is 1.

Q: How can you calculate a missing side in a right triangle?

Depending on the given information, you can use sine, cosine, or tangent to find the missing side. Apply the appropriate trigonometric ratio equation and solve for the unknown side.

Q: Can you calculate the value of an angle in a right triangle?

Yes, if you have the lengths of two sides, you can use inverse trigonometric functions (such as arctan) to find the measure of an angle.

Summary & Key Takeaways

• Trigonometric ratios (sine, cosine, tangent) can be calculated in a right triangle using the lengths of its sides.

• The SOHCAHTOA method states that sine is the opposite side divided by the hypotenuse, cosine is the adjacent side divided by the hypotenuse, and tangent is the opposite side divided by the adjacent side.

• Special right triangles (30-60-90 and 45-45-90) can be used to quickly calculate trigonometric ratios for specific angles.