By William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)
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Additional resources for Analytic Trigonometry
If cot Θ = 3, find all other functions of Θ. 5. From a diagram determine the other four functions of 0 if tan Θ = f, sec 0 = — 4. 6. If sin 0 = 4 and tan Θ is positive, find all the functions of 0. 7. If sin 0 = — ~2 and cos Θ is positive, find all the functions of Θ. 8. If sin Θ = f and r = 36, find x. 9. If cos Θ = f and x = 10,find>\ 10. If csc Θ = b and tan 0 = c, find sin 0 and cot 0. 9. Tables of Trigonometric Functions We have seen that functions of certain special angles can be determined easily by constructing and labelling appropriately the reference triangle.
Find without using tables the value of sin 75°. 2. ), where a and ß are acute. 3. Show that Λ/Ϊ sin (0 - 45°) = sin 0 - cos 0 4. Reduce the following: (a) sin (270° + 0). (b) cos (180° - 0). (c) tan (270° - 0). 5. Express as cofunctions of the corresponding complementary angle: (a) sin 85°. (b) cos 72°. (c) tan 55°. 6. Express as functions of 2 a and 3 β: (a) sin (2 a + 3 β). (b) cos (2 a - 3 β). (c) tan (2 a - 3 β). 7. ), and cot (α — β) from the formulas for the sines and cosines of sums. 8. Derive the reduction formula for tan (α — β) from the reduction formula for tan (α + β\ 9.
2 π. 8. - f π. 315°. 10. - 60°. 11. - 135°. 405°. 13. - \ . 4 14. 240°. 15. - 120°. 8. Functions Determined from a Known Function When one function of an angle is given and the quadrant is 36 ANALYTIC TRIGONOMETRY known, all other functions of the angle may be determined without knowing the angle. Two methods are now available by which this may be done. 5. 7. Example 1. Find the other functions of 0 if cos Θ = £ and Θ is an angle in quadrant II. x Since cos Θ = - and r is positive, we choose r = 5 and then x = — 3.
Analytic Trigonometry by William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)