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- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/02%3A_Graphs_of_the_Trigonometric_Functions/2.04%3A_Graphs_of_the_Other_Trigonometric_FunctionsThat is, what is the domain and what is the range of the tangent function, and what happens to the values of the tangent function at the points that are near points not in the domain of the tangent fu...That is, what is the domain and what is the range of the tangent function, and what happens to the values of the tangent function at the points that are near points not in the domain of the tangent function? That is, what is the domain and what is the range of the secant function, and what happens to the values of the secant function at the points that are near points not in the domain of the secant function?
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/06%3A_Some_Geometric_Facts_about_Triangles_and_ParallelogramsThis appendix contains some formulas and results from geometry that are important in the study of trigonometry.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/03%3A_Triangles_and_Vectors/3.01%3A_Trigonometric_Functions_of_AnglesAs was stated at the start of Chapter 1, trigonometry had its origins in the study of triangles. In fact, the word trigonometry comes from the Greek words for triangle measurement. We will see that we...As was stated at the start of Chapter 1, trigonometry had its origins in the study of triangles. In fact, the word trigonometry comes from the Greek words for triangle measurement. We will see that we can use the trigonometric functions to help determine lengths of sides of triangles or the measure on angles in triangles. As we will see in the last two sections of this chapter, triangle trigonometry is also useful in the study of vectors.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/01%3A_The_Trigonometric_Functions/1.05%3A_Common_Arcs_and_Reference_ArcsIn the beginning activity for this section and in Exercises 1.21 and 1.22, we saw that we could relate the coordinates of the terminal point of an arc of length greater than \(\dfrac{\pi}{2}\) on the ...In the beginning activity for this section and in Exercises 1.21 and 1.22, we saw that we could relate the coordinates of the terminal point of an arc of length greater than \(\dfrac{\pi}{2}\) on the unit circle to the coordinates of the terminal point of an arc of length between \(0\) and \(\dfrac{\pi}{2}\) on the unit circle.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/03%3A_Triangles_and_Vectors/3.06%3A_Vectors_from_an_Algebraic_Point_of_ViewWe have seen that a vector is completely determined by magnitude and direction. So two vectors that have the same magnitude and direction are equal. That means that we can position our vector in the p...We have seen that a vector is completely determined by magnitude and direction. So two vectors that have the same magnitude and direction are equal. That means that we can position our vector in the plane and identify it in different ways. Vectors also have certain geometric properties such as length and a direction angle. With the use of the component form of a vector, we can write algebraic formulas for these properties.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/02%3A_Graphs_of_the_Trigonometric_Functions/2.01%3A_Graphs_of_the_Cosine_and_Sine_FunctionsThe most basic form of drawing the graph of a function is to plot points. One thing we can observe from the graphs of the sine and cosine functions is that the graph seems to have a “wave” form and t...The most basic form of drawing the graph of a function is to plot points. One thing we can observe from the graphs of the sine and cosine functions is that the graph seems to have a “wave” form and that this “wave” repeats as we move along the horizontal axis.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/04%3A_Trigonometric_Identities_and_Equations/4.02%3A_Trigonometric_EquationsA trigonometric equation is a conditional equation that involves trigonometric functions. If it is possible to write the equation in the form “some trigonometric function of x ” = a number.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/05%3A_Complex_Numbers_and_Polar_Coordinates/5.02%3A_The_Trigonometric_Form_of_a_Complex_NumberMultiplication of complex numbers is more complicated than addition of complex numbers. To better understand the product of complex numbers, we first investigate the trigonometric (or polar) form of a...Multiplication of complex numbers is more complicated than addition of complex numbers. To better understand the product of complex numbers, we first investigate the trigonometric (or polar) form of a complex number. This trigonometric form connects algebra to trigonometry and will be useful for quickly and easily finding powers and roots of complex numbers.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/03%3A_Triangles_and_Vectors
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/03%3A_Triangles_and_Vectors/3.03%3A_Triangles_that_are_Not_Right_TrianglesThere are many triangles without right angles (these triangles are called oblique triangles). Our next task is to develop methods to relate sides and angles of oblique triangles. In this section, we w...There are many triangles without right angles (these triangles are called oblique triangles). Our next task is to develop methods to relate sides and angles of oblique triangles. In this section, we will develop two such methods, the Law of Sines and the Law of Cosines. In the next section, we will learn how to use these methods in applications.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Trigonometry_(Sundstrom_and_Schlicker)/01%3A_The_Trigonometric_Functions/1.06%3A_Other_Trigonometric_FunctionsWe defined the cosine and sine functions as the coordinates of the terminal points of arcs on the unit circle. As we will see later, the sine and cosine give relations for certain sides and angles of ...We defined the cosine and sine functions as the coordinates of the terminal points of arcs on the unit circle. As we will see later, the sine and cosine give relations for certain sides and angles of right triangles. It will be useful to be able to relate different sides and angles in right triangles, and we need other circular functions to do that. We obtain these other circular functions – tangent, cotangent, secant, and cosecant – by combining the cosine and sine together in various ways.
