Consider the angles in quadrant 2 and in quadrant 1. (a) Write an expression in terms...

  

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Consider the angles in quadrant 2 and in quadrant 1. (a) Write an expression in terms of and for the difference of the two angles. (b) Can we say for certain which quadrant the difference of the two angles falls in? Why or why not? 13. Two segments are drawn: one from the origin to the point (1, 1), and the second from the origin to the point (43,4). What is the (smaller) angle between the two segments? 14. Verify the identity: (a) sin(x + y) sin(x - y) = 1+sin a-sina 2 (b) cos a sin = cos x + tan x sin 0 1+cos 0 cos ( + sin 0 (d) tan x + cotx = secx csc x (e) secx + tanx = = csc 0 cos x 1-sina -X- sin y 15. Determine a + 3 if a and 3 are acute angles such that: 16. Solve: 17. Verify the identities: (a) 1+sin (b) (tan x + 1)(cosx - 1): (c) tan x = (d) cot0 1+csc0 = = sin a + sin 3 (a) 7 cos x + 5 = 4 (b) 7 cos(2x) + 5 = 4 (c) 7 cos(3x) + 5 = 4 (d) How do your answers to the equations differ? 1-sin a cosx 1-sin 0 sin 0 == tan x tan x sec x - tan x = LIN and cos acos B = 2 Consider the angles in quadrant 2 and in quadrant 1. (a) Write an expression in terms of and for the difference of the two angles. (b) Can we say for certain which quadrant the difference of the two angles falls in? Why or why not? 13. Two segments are drawn: one from the origin to the point (1, 1), and the second from the origin to the point (43,4). What is the (smaller) angle between the two segments? 14. Verify the identity: (a) sin(x + y) sin(x - y) = 1+sin a-sina 2 (b) cos a sin = cos x + tan x sin 0 1+cos 0 cos ( + sin 0 (d) tan x + cotx = secx csc x (e) secx + tanx = = csc 0 cos x 1-sina -X- sin y 15. Determine a + 3 if a and 3 are acute angles such that: 16. Solve: 17. Verify the identities: (a) 1+sin (b) (tan x + 1)(cosx - 1): (c) tan x = (d) cot0 1+csc0 = = sin a + sin 3 (a) 7 cos x + 5 = 4 (b) 7 cos(2x) + 5 = 4 (c) 7 cos(3x) + 5 = 4 (d) How do your answers to the equations differ? 1-sin a cosx 1-sin 0 sin 0 == tan x tan x sec x - tan x = LIN and cos acos B = 2