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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/01%3A_Functions_and_Graphs/1.03%3A_Trigonometric_Functions/1.3E%3A_Exercises_for_Section_1.3This page contains exercises on angle conversions, trigonometric functions, triangle side calculations, and solving identities. It covers sine and cosine equations, including amplitude, period, and ph...This page contains exercises on angle conversions, trigonometric functions, triangle side calculations, and solving identities. It covers sine and cosine equations, including amplitude, period, and phase shifts, along with applications in geometry, angular speed, and natural phenomena models. Additionally, it features mathematical models predicting temperature and tide height with their respective amplitudes and periods, complemented by graphs illustrating their periodic variations.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)This trigonometry textbook this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read...This trigonometry textbook this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section.
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Beveridge)Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships betw...Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high sch...This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/05%3A_Differential_Calculus_with_Parametric_Curves/5.02%3A_Differential_Calculus_of_Parametric_Curves/5.2.01%3A_Exercises_for_Section_5.2\( x=t+\dfrac{1}{t}, \quad y=t−\dfrac{1}{t}, \quad \text{for }t=1\) For \( x=\sin(2t), \quad y=2\sin t\) where \( 0≤t<2π.\) Find all values of \(t\) at which a horizontal tangent line exists. For the ...\( x=t+\dfrac{1}{t}, \quad y=t−\dfrac{1}{t}, \quad \text{for }t=1\) For \( x=\sin(2t), \quad y=2\sin t\) where \( 0≤t<2π.\) Find all values of \(t\) at which a horizontal tangent line exists. For the curve \( x=4t, \quad y=3t−2,\) find the slope and concavity of the curve at \( t=3\). Find intervals for \(t\) on which the curve \( x=3t^2, \quad y=t^3−t\) is concave up as well as concave down.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.07%3A_LHopitals_Rule/4.7E%3A_Exercises_for_Section_4.7This page discusses various limit evaluations in calculus, focusing on different forms and techniques including L'Hôpital's Rule. It highlights key results, such as limits of exponential and logarithm...This page discusses various limit evaluations in calculus, focusing on different forms and techniques including L'Hôpital's Rule. It highlights key results, such as limits of exponential and logarithmic functions, along with polynomial expressions. Specific limits are solved, for example, limits approaching 1, 0, and infinity. The text also addresses scenarios where L'Hôpital's Rule is not directly applicable but suggests reformulations.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.02%3A_Trigonometric_Integrals/3.2E%3A_Exercises_for_Section_3.2This page outlines exercises on trigonometric identities, integrals, u-substitution, and definite integrals, focusing on key identities and methods. It also addresses calculus problems involving funct...This page outlines exercises on trigonometric identities, integrals, u-substitution, and definite integrals, focusing on key identities and methods. It also addresses calculus problems involving function integration, area determination, average values, and differential equations. The text emphasizes the evaluation of trigonometric functions, orthogonality, and provides solutions and techniques for solving these mathematical problems efficiently.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/05%3A_Linear_Transformations/5.04%3A_Special_Linear_Transformations_in_Two_and_Three_DimensionsIn this section, we will examine some special examples of linear transformations in \(\mathbb{R}^2\) including rotations, reflections., and projections.
