MCR 3U Final Exam Review: Trigonometric Functions Special Angles

MCR 3U Final Exam Review: Trigonometric Functions Special Angles Determine the exact value of “x” x 7cm

MCR 3U Final Exam Review: Trigonometric Functions

MCR 3U Final Exam Review: Trigonometric Functions

MCR 3U Final Exam Review: Trigonometric Functions

MCR 3U Final Exam Review: Trigonometric Functions What is the CAST Rule?

MCR 3U Final Exam Review: Trigonometric Functions What are the Primary and Reciprocal Trig Ratios?

MCR 3U Final Exam Review: Trigonometric Functions

MCR 3U Final Exam Review: Trigonometric Functions

MCR 3U Final Exam Review: Trigonometric Functions Point P(5, -2) is on the terminal arm of an angle. a) Determine the primary and reciprocal trig ratios b) Determine the value of the related acute angle to the nearest degree. c) What is the value of the principal angle to the nearest degree?

MCR 3U Final Exam Review: Trigonometric Functions What is the Sine Law?

MCR 3U Final Exam Review: Trigonometric Functions What is the Ambiguous Case? One Triangle ExistsTwo Triangles ExistNo Triangle Exists  The “Swinging arm” is equal to the height  The “swinging arm” is equal to or greater than the other known side  The “Swinging arm” is greater than the height of the triangle  The “Swinging arm” is less than the height of the triangle

MCR 3U Final Exam Review: Trigonometric Functions What are the 5 Trig Identities?

MCR 3U Final Exam Review: Trigonometric Functions Prove the following identity:

MCR 3U Final Exam Review: Trigonometric Functions Periodic Functions: Period – Cycle – Amplitude – Equation of the Axis - The interval of the independent variable (on the x- axis, often time) needed for a repeating action to repeat one cycle. A series of events that are regularly repeated; One complete repetition of the pattern. Half the distance between the maximum and minimum values of a periodic function The equation of the horizontal line halfway between the maximum and the minimum.

MCR 3U Final Exam Review: Trigonometric Functions Identify the period, cycle, amplitude, equation of the axis

MCR 3U Final Exam Review: Trigonometric Functions Graph Sin x and Cos x

MCR 3U Final Exam Review: Trigonometric Functions f(x) = 4 cos [0.25(x - 90°)] + 5 For the above equation, identify: Minimum: Maximum: Amplitude: Equation of the Axis: Period:

MCR 3U Final Exam Review: Trigonometric Functions Graph: f(x) = 0.5 sin [2(x + 30°)] - 1

MCR 3U Final Exam Review: Trigonometric Functions Determine 2 equations for this graph:

MCR 3U Final Exam Review: Trigonometric Functions The depth, d, of water in a harbour on a given day can be modelled by the function: d = 12 sin [30(t – 5)] + 14, Where t is the time past midnight in hours. a)Determine max and min water levels? b)What is the Period? c)Suppose the max changed to be 22m and the minimum changed to be 6m. If the first high tide occurred at 5:00a.m., write the new equation.

MCR 3U Final Exam Review: Trigonometric Functions Review Questions  Pg. 318 #5  Pg. 339 #7  Pg. 354 #7, 8  Pg. 405 #9  Pg. 408 #5, 6, 11, 14, 15, 16, 18, 20, 23