IB Questionbank Maths SL1UNIDAD EDUCATIVA MONTE TABOR NAZARETrea de MatemticasContenido:Caligrafa: Presentacin:Ortografa:AIC # 1 (Ecuaciones trigonomtricas)2015 - 201610NOMBRE: ______________________________ CURSO: III BACH FECHA: ________________ PROFESOR/A: ________________1.(a)Given that 2 sin2 + sin 1 = 0, find the two values for sin .(4)(b)Given that 0 360 and that one solution for is 30, find the other two possible values for .(2)(Total 6 marks)2.Consider y = sin.(a)The graph of y intersects the x-axis at point A. Find the x-coordinate of A, where 0x.(b)Solve the equation sin= , for 0 x 2p.Working:Answers:(a)..................................................................(b)..................................................................(Total 6 marks)3.Consider the trigonometric equation 2 sin2 x = 1 + cos x.(a)Write this equation in the form f (x) = 0, where f (x) = a cos2 x + b cos x + c,and a, b, c .(b)Factorize f (x).(c)Solve f (x) = 0 for 0 x 360.Working:Answers:(a)..................................................................(b)..................................................................(c)..................................................................(Total 6 marks)4.(a)Write the expression 3 sin2 x + 4 cos x in the form a cos2 x + b cos x + c. (b)Hence or otherwise, solve the equation3 sin2 x + 4 cos x 4 = 0,0 x 90.Working:Answers:(a)..................................................................(b)..................................................................(Total 4 marks) 5.Solve the equation 3 sin2 x = cos2 x, for 0 x 180.Working:Answer:......................................................................(Total 4 marks)6. Solve sin 2x = cos x, 0 x .(Total 6 marks)