Evaluate all trig functions from a given point on the terminal side ex1

TL;DR

This video explains how to find the values of six trigonometric functions for a given point on the terminal side of an angle.

Transcript

okay we're giving the point five come on negative top and we know that point it's on the terminal side of the angle theta first we are going to make a sketch of angle theta of course theta I should be interested in the position next we're going to figure out the values of all these six trig functions let's go ahead and get to work right here when w... Read More

Key Insights

• 🔺 The values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) can be found for a given point on the terminal side of an angle.
• 👉 Creating a right triangle using the x and y values of the given point allows for the calculation of the hypotenuse (R) using the Pythagorean theorem.
• 🙃 Sine, cosine, and tangent are found by dividing the corresponding sides of the right triangle by the hypotenuse, while cosecant, secant, and cotangent are obtained by taking the reciprocals of the sine, cosine, and tangent values respectively.

Questions & Answers

Q: How do you find the values of the six trigonometric functions for a given point?

To find the values, create a right triangle using the x and y values of the given point. Determine the hypotenuse using the Pythagorean theorem. Then, divide the corresponding sides of the right triangle by the hypotenuse to find the values of sine, cosine, and tangent. The values of cosecant, secant, and cotangent can be obtained by taking reciprocals of the sine, cosine, and tangent values respectively.

Q: What is the significance of the hypotenuse in finding the trigonometric function values?

The hypotenuse represents the distance from the origin to the given point. It is crucial in calculating the values of sine, cosine, and tangent as these functions involve dividing the lengths of sides by the hypotenuse. The hypotenuse can be found using the Pythagorean theorem, which allows for accurate calculations of the trigonometric functions.

Q: How do you determine the values of cosine and secant in relation to the given point?

The values of cosine and secant are determined by dividing the x value of the given point by the hypotenuse. Cosine represents the ratio of the length of the adjacent side to the hypotenuse, while secant is the reciprocal of cosine. By dividing x by the hypotenuse, the values of cosine and secant can be obtained.

Q: What is the significance of the angle theta in this context?

The angle theta represents the angle between the positive x-axis and the terminal side that passes through the given point. It is essential in determining the trigonometric function values as each function is dependent on the position and measurements of this angle.

Summary & Key Takeaways

• The video demonstrates the process of finding the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for a given point on the terminal side of an angle.

• By creating a right triangle using the x and y values of the given point, the hypotenuse (represented as R) can be determined using the Pythagorean theorem.

• The values of sine, cosine, and tangent are then calculated by dividing the corresponding sides of the right triangle by the hypotenuse, while the values of cosecant, secant, and cotangent are obtained by taking the reciprocals of the sine, cosine, and tangent values respectively.