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fullturn
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in Trigonometric Functions
> Real Exponential, Logarithmic, and Trigonometric Functions for Physicists
Published: August 2022
FIG. 13.2 The trigonometric circle, showing the positive angle of “π/4” ( R fullturn / 8 ) and also the negative angle of “−π/4” ( − R fullturn / 8 ). Note that in the figure, “rad” stands for “radians.” More about this image found in The trigonometric circle, showing the positive angle of “π...
Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_011
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
..., and R3. We will now prove that (11.1) ∠ 1 , ∠ 2 , ∠ 3 are the interior angles of a triangle ⟹ ∡ 1 + ∡ 2 + ∡ 3 = R fullturn / 2. proof Case: Fig. 11.2 ∡ 5 + ∡ 6 + ∡ 4 = R fullturn / 2 [Eqs. (10.75) and (10.78...
Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_010
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
... (see Fig. 10.12 ) have, respectively, a measure of “0” (zero) and a measure equal to a positive real number that, in this book, we will refer to as “ R fullturn ” ( R fullturn > 0 ; R fullturn is equal to the measure of one “full turn” or one “complete rotation...
Images
Published: August 2022
FIG. 10.12 A ray GRy with starting point P0; additionally, the angle ∠ 2 that is one of the two angles determined by the ray GRy and itself; note that ∡ 2 = R fullturn . More about this image found in A ray GRy with starting point ...
Images
Published: August 2022
FIG. 10.19 Two perpendicular lines GLn1 and GLn2. Also shown are the four angles determined by the intersection of GLn1 and GLn2: ∠ 1 , ∠ 2 , ∠ 3 , and ∠ 4 . Note that ∡ 1 = ∡ 2 = ∡ 3 = ∡ 4 = R fullturn / 4 . More about this image found in Two perpendicular lines GLn1 a...
Images
Published: August 2022
FIG. 10.16 Two distinct lines GLn1 and GLn2 that intersect at point P. Additionally, the four angles ∠ 1 , ∠ 2 , ∠ 3 , and ∠ 4 determined by the two lines GLn1 and GLn2. Also note that ∡ 1 + ∡ 2 + ∡ 3 + ∡ 4 = R fullturn . More about this image found in Two distinct lines GLn1 and ...
Images
Published: August 2022
FIG. 10.14 Two non-collinear rays GRy1 and GRy2 that have the same starting point P0; additionally, the two angles ∠ 1 and ∠ 2 determined by the two rays. Note that ∡ 1 + ∡ 2 = R fullturn . Also note that ∠ 1 is convex and ∠ 2 is concave. More about this image found in Two non-collinear rays GRy...
Images
Published: August 2022
FIG. 10.17 Two distinct lines GLn1 and GLn2 that intersect at point P. Additionally, the two adjacent angles ∠ 1 and ∠ 2 ; as well as the two opposite angles ∠ 1 and ∠ 3 . Additionally shown is angle ∠ T o t 1 determined by the two rays with starting point P that are on line GLn1; and angle ∠ T o t 2 determined by the two rays with starting point P that are on line GLn2. Note that ∡ 1 + ∡ 2 = R fullturn / 2 and also that ∡ 1 = ∡ 3 . More about this image found in Two distinct lines GLn1 and ...
Images
Published: August 2022
FIG. 10.13 Two distinct collinear rays G R y 1 = P 0 P 1 → and G R y 2 = P 0 P 2 → that have the same starting point P0; additionally, the two angles ∠ 1 and ∠ 2 determined by the two rays. Note that ∡ 1 = ∡ 2 = R fullturn / 2 . Also note that G R y 1 ∩ G R y 2 = { P 0 } and G R y 1 ∪ G R y 2 = G L n . More about this image found in Two distinct collinear rays G R y 1 = P 0 ...
Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_013
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
... are a negative real number) (see Figs. 13.2 and 13.3 ). FIG. 13.2 The trigonometric circle, showing the positive angle of “π/4” ( R fullturn / 8 ) and also the negative angle of “−π/4” ( − R fullturn / 8 ). Note that in the figure, “rad” stands for “radians...