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Write the coordinates P(x, y) Factor x2 5x 6 x 3 x 2 3 x 2 14 x 5 3x 1 x 5 sin 2 1 sin 2 2 sin cos 6 6 2 sin 2 5sin 6 0 Trigonometric Expressions Trigonometric Equations Rewrite the equation to isolate the trig function. Solve for the angle within the given domain. Write the general solution. a ) 2sin 1 0 2sin 1 1 sin 2 0 360 b) 4 cos 1 cos 3cos 1 y is positive I or II special ratio ref angle 30° 30 or 150 1 cos 3 0 2 x is negative II or III not special ratio ref angle 1.23 1.91 or 4.37 30 360 n, n I 1.91 2 n, n I 150 360 n, n I 4.37 2 n, n I c) 3 csc 2 0 0 360 3 csc 2 2 csc 3 3 y is negative sin 2 III or IV 0 2 d ) 4sec 3 3sec 2 sec 1 cos 1 x is - 1 quadrantal angle special ratio ref angle 60° 2400 or 300 240 360 n, n I 300 360 n, n I 2 n, n I Solve for if 0 ≤ < 2. 1 2 a) sin 4 b) cs c 3 2 2 1 sin 2 1 sin 2 y is negative or positive 2 sin 2 Reference r Angle 4 csc 3 I, II, III or IV 4 3 5 7 4 , 4 , 4 , 4 2 csc 3 y is negative or positive I, II, 3 III or IV sin 2 Reference r Angle 3 2 4 5 , , , 3 3 3 3 Solving Trigonometric Equations c) 4sin2 x - 3 = 0 4sin2 x = 3 2 4 5 x , , , 3 3 3 3 3 sin x 4 2 3 sin x 4 3 sin x 2 Reference Angle xr 0 ≤ < 2. 3 y is negative or positive I, II, III or IV 4 2 n, n I 0 ≤ < 2. Solving Second Degree Trigonometric Equations d) 2 sin2 sin 0 sin (2sin 1) 0 sin 0 or 2sin 1 0 quadrantal 1 sin 2 Reference r Angle 6 0, , 7 , 11 6 6 y is negative III or IV e) 2 sin2 sin 1 0 (2 sin 1)(sin 1) 0 2 sin 1 0 or sin 1 0 1 sin or sin 1 2 Reference r Angle 6 5 3 , , 6 6 2 Solving Trigonometric Equations 0 ≤ < 2. f) 2 cos2 7cos 3 0 (2 cos 1)(cos 3) 0 2 cos 1 0 or cos 3 0 1 cos 3 cos or Reference Angle 2 3 5 , 3 3 NO solution for cos = 3. 0 ≤ x < 360° g) (sin x 1)(tan x 1) 0 sin x 1 0 tan x 1 0 sin x 1 tan x 1 x 90 x 45 Page 211 1b, 2, 3, 4a,b, 5, 7, 9, 10, 11, 12, 18, 19