Academic Trigonometry Plane And Spherical

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The diagonals of a rhombus bisect at right angles. Half sum = greater — half difference.
sin ^ + sin 5 = 2 YY' = 2 sin ^ VY'.
5. (cos A — cos By-\- (sin A — sin By — 4 sin' 6. Cos2^ = (l-tanM) : (l + tan^^).
7. As27rr = 360°, r° = — =57. 3.
TT iA-B How many degrees in L5r? Ans.
270^ What is the length of 80°, r being the unit?
Ans. -^ = |7r. 57. 3 ^ 8. If 1^= cos^H- -sin^, . -. Cos J. = ^^^ ~^, and sin ^ -^, 1^ X Is being 1(^+5)5 and the binomial formula 1 holding for such quantity, find sin(^l
... + ^), cos(^4-7^), sinu4 + sin5, etc. , including cos 2 J. , sin 3 J. , cos 4^, -f. = 4-V — 1. 1^= initial cos A + transverse sin A.
9. The earth's radius subtends an angle of 57' at the moon ; what is the distance (by 7) ? The moon's apparent diameter is 31' ; what is it in miles (by 7) ?
EXERCISES. 23 10. Construct the figure of page 13 : (1) When one side is in I, and the other in II.
(2) When both are in II, . -. H in I.
11. Construct the figure of page 19 : (1) When A and B are in I, but (^ + -B) in II.


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