ACT PREP Mathematics Trigonometry DON'T FORGET CALCULATOR! MODE: DEGREES! Mathematics Trigonometry TRIGONOMETRY Overview Trigonometry (7%). Questions in this content area are based on understanding trigonometric relations in right triangles; values and properties
of trigonometric functions; graphing trigonometric functions; modeling using trigonometric functions; use of trigonometric identities; and solving trigonometric equations. Topic Basic Skills Application
2 2 0 4 TRIGONOMETRY Trigonometric Functions for special angles
undefined TRIGONOMETRY- THE UNIT CIRCLE ALL POINTS ON THE CIRCLE ARE REPRESENTED BY (COS, SIN Quadrants 1 Degree = 1/360 of a revolution (full circle) Radians o Angle with arc length = r o 1 degree = /180 radians o 1 radian = 180o/
98% of the time, this is given in the problem! TRIGONOMETRY- THE UNIT CIRCLE EXAMPLES 1. What quadrant is the angle 210o? 2. How about radians? A TOUGH ONE: If , what is the value of sin
TRIGONOMETRY Coterminal Angles Angles that common terminal and initial sides Add or subtract multiple of 360o (2 for radians) to find coterminal angles
TRIGONOMETRY Six Trigonometric Ratios TRIGONOMETRY Graph of Sin(x) TRIGONOMETRY Graph of Cos(x) TRIGONOMETRY
Graph of Tan(x) TRIGONOMETRY Trig Identities for any trig value (not just right triangles!) Example: Find tanx if sinx = and cosx = 1/3 TRIGONOMETRY Solving Nonright Triangles (pg. 308) TRIGONOMETRY
Practice Problems Which of the following is the sine of A in the right triangle below? A. 5/13 B. 5/12 C. 12/13 D. 12/5 E. 13/5
Which of the following expressions is the closest approximation to the height h, in feet, of the roof truss shown below? A. 15 tan 20 B. 15 sin 20
C. 30 tan 20 D. 30 sin 20 E. 15/sin 20 In the figure below, points A and B are on opposite banks of a small stream. Point C is on the same bank of the stream as point B and approximately 18 meters from B. The measure of CBA is 45, and the measure of BCA is 60. Which of the following expressions gives the approximate distance, in meters, between point A and point B ?(Note: For PQR, where p, q, and r are the lengths of the sides opposite P, Q, and R, respectively, sinP/p=sinQ/q=sinR/r.)
-A. sin60/18sin45 -B. sin60/18sin75 -C. 18sin45/sin60 -D. 18sin60/sin45 -E. 18sin60/sin75 TRIGONOMETRY Practice Problems Which of the following is equivalent to sin(x) csc(x) wherever sin(x) csc(x) is defined?
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