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**Extra resources for Plane and Spherical Trigonometry**

**Example text**

4 Ans. 9302. ' 3 x i" + sin x . 534a2. quadrant, show that vers (0 - 11") = \\". 80. If cot 250° = ~, show that tan 160° = -~, and sec 430° = Vl+b'. 81 . If covers 115 ° -- I -! e find vers 205° cos 335°. -. -- v0-=1. A ns. - cos 250°. Ans. C C2 + ( sin 250° + tan 290. 83. If csc 160° = c, find Ans. -1. cot 200° + cos 340°' Draw the figures and derive the formulas in each of the following: 84. Functions of 90° + 0 in terms of functions of 0 when 0 is in the third quadrant. 86. Functions of 270° - 0 in terms of functions of 0 when 0 is in the second quadrant.

Cas 25°. x = -- l' = -cas l' - 1" Fig. 50, OP, and - tan (V B) = y' "Xi = y = -- l' l' x y= cot B. = -sin B. - B. B. x cot (t'll" - B) = x' = Y = tan B. sec (~'II" - B) = csc (V - B) = x 1" "Xi r' 11 l' l' r r = - y = - Jj csc = =x = -x = -sec B. Notice that here again in each line the function at the end is the cofunction of the one at the beginning. -sin 250° = sin (270° - 20°) = -cas 20°. tan 210° = tan (270° - 60°) = cot 60°. FIG. 50. since x' csc l' 11 Y Then, = --x = -- x = - sec B. -y cas (2a'll"- B) = x' - = -cas 20°.

Ans. 2'. 41. Suppose the earth a sphere with a radius of 3960 miles; find the length of the arctic circle which is at latitude 66° 32'. Ans. 3 miles. 42. Find the length of 1 ° of longitude in the latitude of Chicago, 41 ° 50', if the earth is a sphere with a radius of 3960 miles. Ans. 497 miles. 43. A circle 12 in. in diameter is suspended from a point and held in a horizontal position by 12 strings each 8 in. long and equally spaced around the circumference. Find the angle between two consecutive strings.