Photo by Annie Spratt on Unsplash Trigonometry : Plane Right
Triangles
Source of Figures and references:
https://openstax.org/details/books/college-algebra.
Engineering Mathematics Vol1, Gillesania
Stewart’s Algebra and Trigonometry
Mathalino.com
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Trigonometry: Plane Right Triangles, Exercises of Mathematics
An overview of the fundamental concepts of trigonometry, focusing on plane right triangles. It covers the definition of a ray, an angle, and the measurement of angles in degrees. The document also introduces the concepts of standard position, positive and negative angles, supplementary angles, complementary angles, and the cofunction identity. The information presented in this document could be useful for students studying topics related to trigonometry, geometry, and mathematics in general. The document could serve as a reference or supplementary material for courses in these areas, providing a solid foundation for understanding the properties and relationships of plane right triangles.
Typology: Exercises
2020/2021
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Photo by Annie Spratt on Unsplash
Trigonometry : Plane Right
Triangles
Source of Figures and references: https://openstax.org/details/books/college-algebra. Engineering Mathematics Vol1, Gillesania Stewart’s Algebra and Trigonometry Mathalino.com
Photo by Peter Gargiulo on Unsplash
Fundamentals
We leave one fixed in place, and rotate the other. The fixed ray is the initial side, and the rotated ray is the terminal side. We indicate the rotation with a small arc and arrow close to the vertex/
The measure of an angle is the amount of rotation from the
initial side to the terminal side.
One degree is 1 360 of a circular rotation, so a complete circular rotation contains 360 degrees. An angle is in standard position if its vertex is located at the origin, and its initial side extends along the positive x-axis. Notation: If the angle is measured in a counterclockwise direction from the initial side to the terminal side, the angle is said to be a positive angle. If the angle is measured in a clockwise direction, the angle is said to be a negative angle.
It is possible for more than one angle to have the same terminal side. Look at Figure 16. The angle of 140° is a positive angle, measured counterclockwise. The angle of −220° is a negative angle, measured clockwise. But both angles have the same terminal side.
Photo by Peter Gargiulo on Unsplash
Right Trigonometry
Supplementary Angle: Two Angles are Supplementary when they add up to 180 degrees. Complementary Angle: Two angles are Complementary when they add up to 90 degrees (a Right Angle
Cofunction identity If any two angles are complementary, the sine of one is the cosine of the other, and vice versa