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- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/10%3A_Right_Triangle_Trigonometry_Angles/10.01%3A_AnglesIn elementary geometry, angles are always considered to be positive and not larger than 360∘. You also learned that the sum of the angles in a triangle equals 180◦, and that an isoscele...In elementary geometry, angles are always considered to be positive and not larger than 360∘. You also learned that the sum of the angles in a triangle equals 180◦, and that an isosceles triangle is a triangle with two sides of equal length. Recall that in a right triangle one of the angles is a right angle. Thus, in a right triangle one of the angles is 90◦ and the other two angles are acute angles whose sum is 90◦ (i.e. the other two angles are complementary angles).
- https://math.libretexts.org/Courses/Riverside_City_College/Random_Course/1%3A_Right_Triangle_Trigonometry_Angles/1.3%3A_Applications_and_Solving_Right_TrianglesThroughout its early development, trigonometry was often used as a means of indirect measurement, e.g. determining large distances or lengths by using measurements of angles and small, known distances...Throughout its early development, trigonometry was often used as a means of indirect measurement, e.g. determining large distances or lengths by using measurements of angles and small, known distances. Today, trigonometry is widely used in physics, astronomy, engineering, navigation, surveying, and various fields of mathematics and other disciplines. In this section we will see some of the ways in which trigonometry can be applied. Your calculator should be in degree mode for these examples.
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/10%3A_Right_Triangle_Trigonometry_Angles/10.05%3A_Rotations_and_Reflections_of_AnglesNow that we know how to deal with angles of any measure, we will take a look at how certain geometric operations can help simplify the use of trigonometric functions of any angle, and how some basic r...Now that we know how to deal with angles of any measure, we will take a look at how certain geometric operations can help simplify the use of trigonometric functions of any angle, and how some basic relations between those functions can be made. The two operations on which we will concentrate in this section are rotation and reflection.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/03%3A_Multiple_IntegralsThe multiple integral is a generalization of the definite integral with one variable to functions of more than one real variable. For definite multiple integrals, each variable can have different limi...The multiple integral is a generalization of the definite integral with one variable to functions of more than one real variable. For definite multiple integrals, each variable can have different limits of integration.
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/01%3A_Right_Triangle_Trigonometry_Angles/1.0E%3A_1.E%3A_Right_Triangle_Trigonometry_Angles_(Exercises)These are homework exercises to accompany Corral's "Elementary Trigonometry" Textmap. This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra...These are homework exercises to accompany Corral's "Elementary Trigonometry" Textmap. 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.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/03%3A_Multiple_Integrals/3.E%3A_Multiple_Integrals_(Exercises)Problems and select solutions to the chapter.
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/05%3A_Graphing_and_Inverse_Functions/5.01%3A_Graphing_the_Trigonometric_FunctionsThe trigonometric functions can be graphed just like any other function, as we will now show. In the graphs we will always use radians for the angle measure.
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/04%3A_Radian_Measure/4.04%3A_Circular_Motion-_Linear_and_Angular_SpeedSo suppose that an object moves along a circle of radius r, traveling a distance s over a period of time t, as in Figure 4.4.1. Then it makes sense to define the (average) linear speed ν of the object...So suppose that an object moves along a circle of radius r, traveling a distance s over a period of time t, as in Figure 4.4.1. Then it makes sense to define the (average) linear speed ν of the object as: v=st. Let θ be the angle swept out by the object in that period of time. Then we define the (average) angular speed ω of the object as: ω = \frac{θ}{ t}.
- https://math.libretexts.org/Bookshelves/Calculus/Elementary_Calculus_2e_(Corral)/01%3A_The_Derivative/1.04%3A_Derivatives_of_Sums_Products_and_Quotients\[\begin{aligned} d(f \cdot g) ~&=~ (f \cdot g)(x + \dx) ~-~ (f \cdot g)(x)\\ &=~ f(x + \dx) \cdot g(x + \dx) ~-~ f(x) \cdot g(x) &\\ &=~ \text{(area of outer rectangle)} ~-~ \text{(area of original r...\[\begin{aligned} d(f \cdot g) ~&=~ (f \cdot g)(x + \dx) ~-~ (f \cdot g)(x)\\ &=~ f(x + \dx) \cdot g(x + \dx) ~-~ f(x) \cdot g(x) &\\ &=~ \text{(area of outer rectangle)} ~-~ \text{(area of original rectangle)}\\ &=~ \text{sum of the areas of the three shaded inner rectangles}\\ &=~ f(x) \cdot \dg ~+~ g(x) \cdot \df ~+~ \df \cdot \dg\\ &=~ f(x) \cdot \dg ~+~ g(x) \cdot \df ~+~ (f'(x)\;\dx) \cdot (g'(x)\;\dx)\\ &=~ f(x) \cdot \dg ~+~ g(x) \cdot \df ~+~ (f'(x) g'(x)) \cdot (\dx)^2\\ &=~ f(x) \cdo…
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/05%3A_Graphing_and_Inverse_Functions/5.02%3A_Properties_of_Graphs_of_Trigonometric_FunctionsWe saw in Section 5.1 how the graphs of the trigonometric functions repeat every 2π radians. In this section we will discuss this and other properties of graphs, especially for the sinusoidal function...We saw in Section 5.1 how the graphs of the trigonometric functions repeat every 2π radians. In this section we will discuss this and other properties of graphs, especially for the sinusoidal functions (sine and cosine).
- https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/01%3A_Right_Triangle_Trigonometry_Angles/1.03%3A_Applications_and_Solving_Right_TrianglesThroughout its early development, trigonometry was often used as a means of indirect measurement, e.g. determining large distances or lengths by using measurements of angles and small, known distances...Throughout its early development, trigonometry was often used as a means of indirect measurement, e.g. determining large distances or lengths by using measurements of angles and small, known distances. Today, trigonometry is widely used in physics, astronomy, engineering, navigation, surveying, and various fields of mathematics and other disciplines. In this section we will see some of the ways in which trigonometry can be applied. Your calculator should be in degree mode for these examples.
