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4 University of Cebu-Main Campus f Sanciangko St., Cebu City, 6000 Philippines university of cebu College of Engineering Tel. no. 255-7777 loc. 4102 MODULE 3: PLANE AND SPHERICAL TRIGONOMETRY Angles 1. Acertain angle has a supplements five times its compliment Find the angle Ans. 67.5 2. If the supplement of a given angle is 5/2 of its complement, find the value of the angle. Ans. 30 Trigonometric Functions and Identities 3. Simplify secO - secOsin20 Ans. cosO 4. IfsinA = 2.571x, cos A = 3.06x and sin 2A = 3.939x, find the value of x. Ans. 3/5 Sinusoidal and Asymptotic Trigonometric Functions 5. Given the function f(x) = 4 cos (3x+4m) - 2, identify the amplitude, period, frequency, phase shift and vertical shift. Ans. Amplitude: 4 20 Period: — 3 Frequency: — 20 4m Phase Shift: - a Vertical shift: -2 6. Given the function y = tan (2x - 1/3) + 2, determine the amplitude, period, frequency, phase shift, vertical shift and asymptote. Ans. Amplitude: undefined . T Period: = 2 2 Frequency: « 2n Phase Shift: a Vertical shift: 2 Asymptote: . (8/6+k) Plane Triangles 7. A tower and a monument stand in a level plan. The angles of depression of the top and bottom of the monument viewed from the top of the tower are 13 and 31 respectively. The height of the tower is 145 ft. find the height of the monument. Ans. 89.29 ft. 8. The angle of elevation of the top of the building B from the top of building A is 28° and the angle of elevation of the top of building A from the base of building B is 46°. If building B is 120m high, determine the height of building A. Assume both building lie in the same horizontal plane. Ans. 79.29m Triangle Inequality and Ambiguity 9. Check whether it is possible to form a triangle with the following measures: 7 units, 4 units, and 5 units. Ans. A triangle 10. In AABC, mzA = 30°,a = 20 and c = 16. How many triangle(s) it forms? Ans. one distinct triangle Spherical Triangles 11. The area of spherical triangle ABC whose parts are A= 93°40’, B= 64°12’, C= 116°51’ and the radius of the sphere is 100m is Ans. 16531 sq. m 12. Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14°36’N, 121°05’E. San Francisco is situated at 37°48’N, 122°24’W. Ans. 6046.2 nautical miles Complex Numbers 13. Whatis the value of (4 - 5i) (12 +111)? Ans. 103 - 16i 14. Simplify: 8i (10 + 2i) Ans. - 16 +80i 
