Sine Cosine Tangent Explained - Right Triangle Basic Trigonometry - sin cos tan sec csc cot

TL;DR

This video explains the basic concepts of sine, cosine, and tangent in trigonometry and demonstrates how to calculate their values.

Transcript

in this video we're going to go over sine cosine and tangent basic trigonometry stuff so let's begin let's start with the right triangle so this is the box which represents the 90 degree angle and let's say this is our angle theta now which side is opposite to theta opposite to theta is this side on the right so that's the opposite side the adjacen... Read More

Key Insights

• 🔺 Trigonometry involves the study of right triangles and the relationships between their sides and angles.
• 🥳 Sine, cosine, and tangent are important ratios used in trigonometry to calculate the ratios of sides in right triangles.
• 🥳 Reciprocal ratios, such as secant, cosecant, and cotangent, are derived from the main trigonometric ratios.
• 🔺 Special triangles, such as the 3-4-5 triangle and 45-45-90 triangle, can be used to find missing side lengths in right triangles.
• ➗ Quadrants, which divide the coordinate plane, play a significant role in determining the signs of trigonometric functions in different quadrants.
• 🆘 Reference angles help determine the appropriate values of trigonometric functions in specific quadrants, considering their restricted domains.

Questions & Answers

Q: What are the main ratios used in basic trigonometry?

The main ratios used in basic trigonometry are sine, cosine, and tangent. They represent the ratios of the sides of a right triangle.

Q: What is the Pythagorean theorem and how is it used in trigonometry?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It is used in trigonometry to find missing side lengths in right triangles.

Q: How can you find the values of other trigonometric functions if sine theta is given?

To find the values of other trigonometric functions, you can use the given value of sine theta along with the relationships between the trigonometric functions. For example, if sine theta is given as 3/5, you can find the values of cosine theta, tangent theta, and other functions based on the given value.

Q: What is a reference angle and how is it used in trigonometry?

A reference angle is the acute angle between the x-axis and the terminal side of an angle. It is used in trigonometry to determine the values of trigonometric functions in different quadrants, as the functions have specific ratios in specific quadrants.

Summary & Key Takeaways

• The video starts by introducing the right triangle, with one angle labeled as theta. It explains the concepts of opposite, adjacent, and hypotenuse sides of the triangle.

• The video then introduces the sine, cosine, and tangent ratios and explains how to calculate them using the SOHCAHTOA abbreviation.

• It covers the reciprocal ratios, such as secant, cosecant, and cotangent.

• The video also discusses special triangles, including the 3-4-5 triangle and 45-45-90 triangle, and how to use them to find missing sides.

• The video explains the concept of quadrants and their relationship to trigonometric functions.

• It concludes with examples of finding values of other trigonometric functions based on given values.