Comprehensive Review of Trigonometry, Vectors, and Right Triangles
This chapter reviews key concepts in trigonometry and vectors, focusing on right triangles. It covers the Pythagorean theorem, SOHCAHTOA for trigonometric relationships, and explores the Law of Sines and Law of Cosines applicable to any triangle. Additionally, it distinguishes between scalar and vector quantities, detailing vector addition, subtraction, and component resolution. Exercises include practical examples, such as determining resultant vectors, enhancing understanding of dimensional analysis in physics. Utilize math resources for further study!
Comprehensive Review of Trigonometry, Vectors, and Right Triangles
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Presentation Transcript
Chapter 1 Trig Review and Vectors
Right Triangles • Pythagorean theorem • Sohcahtoa Caution! These relationships exist ONLY for right triangles!
Law of Sines a,b, c are lengths of sides A, B, and C all represent angles Try a few examples with this triangle
Law of Cosines You can use this law and the law of sines for ANY triangle!
Other Math Reminders • Don’t forget the quadratic equation… someday I’ll learn the song. • Alternate interior angles • 3,4,5 triangles • Angles add up to 180⁰ • Use the appendix, math text books, and internet for math review as needed! • Dimensional Analysis
Vectors • In physics, measurable quantities are referred to as either scalaror vector • Scalar quantities are those quantities not associated with a direction • Vector quantities include both magnitude and direction
Vector vs. Scalar • Scalar quantities • Time • Distance • Speed • Temperature • Vector quantities • Force • Displacement • Velocity • Acceleration • Momentum
Vector Addition • Add vectors graphically using a ruler and protractor • ALWAYS add vectors using the head-to-tail method • Vector magnitudes must be scaled to the magnitude of the quantity being represented. • Vectors can also be added using geometry and trig • When doing this, a ruler and protractor is not always necessary • Vector components can be used for more complicated addition
Vector Subtraction • When subtracting vectors, use the same method as addition • The only difference is that you will be reversing the direction of the subtracted vector
Vector Components • All vectors can be “resolved into components.” • Simply put, vectors have an x- and y- component. • Usually, sohcahtoa is used to help determine these components • Most helpful for the addition of more than one vector
Addition of Vectors A jogger runs 145m in a direction 20.0⁰east of north and then 105m in a direction 35.0⁰ south of east. Determine the magnitude and direction of the resultant vector using three methods! YES, use all three this time.
