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- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/zz%3A_Back_Matter
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/03%3A_Trigonometric_Identities_and_Equations/3.05%3A_Double_Angle_Identities\[\begin{array}{l} {\cos \left(2\alpha \right)=\cos (\alpha +\alpha )} \\ {\cos (\alpha )\cos (\alpha )-\sin (\alpha )\sin (\alpha )} \\ {\cos ^{2} (\alpha )-\sin ^{2} (\alpha )} \end{array}\nonumber\...\[\begin{array}{l} {\cos \left(2\alpha \right)=\cos (\alpha +\alpha )} \\ {\cos (\alpha )\cos (\alpha )-\sin (\alpha )\sin (\alpha )} \\ {\cos ^{2} (\alpha )-\sin ^{2} (\alpha )} \end{array}\nonumber\] Rearranging the Pythagorean Identity results in the equality \(\cos ^{2} (\alpha )=1-\sin ^{2} (\alpha )\), and by substituting this into the basic double angle identity, we obtain the second form of the double angle identity.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/00%3A_Front_Matter
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/01%3A_Right_Triangles_and_an_Introduction_to_Trigonometry/1.05%3A_Measuring_RotationSince our angle is more than one rotation, we need to add \(360^{\circ}\) until we get an angle whose absolute value is less than \)\(360^{\circ}\): \(−745^{\circ}+360^{\circ}=−385^{\circ}\), again \(...Since our angle is more than one rotation, we need to add \(360^{\circ}\) until we get an angle whose absolute value is less than \)\(360^{\circ}\): \(−745^{\circ}+360^{\circ}=−385^{\circ}\), again \(−385^{\circ}+360^{\circ}=−25^{\circ}\). Since the terminal side lies in the third quadrant, we need to find the angle between \(180^{\circ}\) and \(235^{\circ}\), so \(235^{\circ}−180^{\circ}=55^{\circ}\).
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.05%3A_Graphing_Tangent_Cotangent_Secant_and_CosecantSuppose the function \(y=5\tan(\dfrac{\pi}{4}t)\) marks the distance in the movement of a light beam from the top of a police car across a wall where \(t\) is the time in seconds and \(y\) is the dist...Suppose the function \(y=5\tan(\dfrac{\pi}{4}t)\) marks the distance in the movement of a light beam from the top of a police car across a wall where \(t\) is the time in seconds and \(y\) is the distance in feet from a point on the wall directly across from the police car.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/College_Mathematics_-_Abridged_Edition/03%3A_Quadratic_Functions/3.01%3A_Graphs_of_Quadratic_FunctionsNotice that the larger the value of a is, the skinnier the graph is – for example, in the first plot, the graph of \(y=3x^2\) is skinnier than the graph of \(y=x^2\). We can see from the graph that th...Notice that the larger the value of a is, the skinnier the graph is – for example, in the first plot, the graph of \(y=3x^2\) is skinnier than the graph of \(y=x^2\). We can see from the graph that the highest value of the area occurs when the length of the rectangle is 25 . The area of the rectangle for this side length equals 625. (Notice that the width is also 25, which makes the shape a square with side length 25 .)
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.02%3A_Applications_of_Radian_MeasureIn general, the radian measure of an angle is the ratio of the arc length cut off by the corresponding central angle in a circle to the radius of the circle, independent of the radius. The above discu...In general, the radian measure of an angle is the ratio of the arc length cut off by the corresponding central angle in a circle to the radius of the circle, independent of the radius. The above discussion says more, namely that the ratio of the length \(s \) of an intercepted arc to the radius \(r \) is preserved, precisely because that ratio is the measure of the central angle in radians (see Figure 2.2.2).
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/zz%3A_Back_Matter/20%3A_GlossaryExample and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pag...Example and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix CC-BY-SA; Delmar Larsen Glossary Entries Definition Image Sample Word 1 Sample Definition 1
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/04%3A_Inverse_Trigonometric_FunctionsThumbnail: inverse of sine graph ( GNU GPL; Michael Corral via LibreTexts).
- https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.01%3A_Radian_MeasureIn Figure 2.1.1 we see that a central angle of \(90^\circ \) cuts off an arc of length \(\tfrac{\pi}{2}\,r \), a central angle of \(180^\circ \) cuts off an arc of length \(\pi\,r \), and a central an...In Figure 2.1.1 we see that a central angle of \(90^\circ \) cuts off an arc of length \(\tfrac{\pi}{2}\,r \), a central angle of \(180^\circ \) cuts off an arc of length \(\pi\,r \), and a central angle of \(360^\circ \) cuts off an arc of length \(2\pi\,r \), which is the same as the circumference of the circle. Formally, a radian is defined as the central angle in a circle of radius \(r \) which intercepts an arc of length \(r \), as in Figure 4.1.2.
