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https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/00%3A_Front_Matter/02%3A_InfoPage
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 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.
3.5: Double Angle Identities
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.
1.5: Measuring Rotation
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_Rotation
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 $...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 $235^{\circ}−180^{\circ}=55^{\circ}$ .
2.5: Graphing Tangent, Cotangent, Secant, and Cosecant
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_Cosecant
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 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.
2.2: Applications of Radian Measure
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.02%3A_Applications_of_Radian_Measure
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 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).
Glossary
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/zz%3A_Back_Matter/20%3A_Glossary
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 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
Chapter 4: Inverse Trigonometric Functions
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/04%3A_Inverse_Trigonometric_Functions
Thumbnail: inverse of sine graph ( GNU GPL; Michael Corral via LibreTexts).
2.1: Radian Measure
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.01%3A_Radian_Measure
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 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.
Chapter 3: Trigonometric Identities and Equations
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/03%3A_Trigonometric_Identities_and_Equations
Thumbnail: Graphs of y=sin(2θ) and y=sin(θ) (CC BY-NC-SA; Ted Sundstrom & Steven Schlicker via LibreTexts).
1.7: Trigonometric Functions of Any Angle
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/01%3A_Right_Triangles_and_an_Introduction_to_Trigonometry/1.07%3A_Trigonometric_Functions_of_Any_Angle
A reference angle is the angle formed between the terminal side of the angle and the closest of either the positive or negative $x$ -axis. In general, if a negative angle has a reference angle of \(3...A reference angle is the angle formed between the terminal side of the angle and the closest of either the positive or negative $x$ -axis. In general, if a negative angle has a reference angle of $30^{\circ}$ , $45^{\circ}$ , or $60^{\circ}$ , or if it is a quadrantal angle, we can find its ordered pair, and so we can determine the values of any of the trig functions of the angle.
5.4: Vectors
https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/05%3A_Triangles_and_Vectors/5.04%3A_Vectors
While adding and subtracting vectors gives us a new vector with a different magnitude and direction, the process of multiplying a vector by a scalar, a constant, changes only the magnitude of the vect...While adding and subtracting vectors gives us a new vector with a different magnitude and direction, the process of multiplying a vector by a scalar, a constant, changes only the magnitude of the vector or the length of the line. Scalar multiplication has no effect on the direction unless the scalar is negative, in which case the direction of the resulting vector is opposite the direction of the original vector.

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