9 Find the values of a and b 39 10 Find the exact value of

9. Find the values of a and b: 39° 10. Find the exact value of : a) (Both u and v are in Quadrant II), Sin(u + u) ; where sin u s and Cos u = 13 12 b) Cos 750 11. Find the values of the six trigonometric functions of -4 Cos& = , sin

Solution

10) a)

        sin(u) = 4/5

       cos(u) = 3/5

        cos(v) = 12/13

        sin(v) = 5/13

sin(u + v) = sinu*cosv + cosu*sinv = (4/5)*(12/13) + (3/5)*(5/13) = 48/65 + 15/65 = 63/65

b) cos75 = cos (30 + 45) = cos30cos45 – sin30sin45 = (3/2)(1/2) – (1/2)(1/2)

                          cos75 = (3 - 1)/(2 2)

11) cos = -4/5

      sin = sqrt(1 – cos²) = -3/5

      tan = sin/cos = ¾

      sec = 1/cos = -5/4

      csc = 1/sin = -5/3

      cot = 1/tan = 4/3

12) f(x) = 4*sin(3x)

(a) Amplitude = 4

(b) Period = 2pi/3