8.1: Graphical Solutions of Trig Functions

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Presentation transcript:

8.1: Graphical Solutions of Trig Functions Worksheet 3 Key 1) –π/2 2) 2π/3 3) –π/6 4) –π/4 5) –1 6) 7) 3/2 8) 𝟏𝟕 𝟏𝟕 9) 𝟏𝟎 10) –π/3 11) 𝟐 𝟐 12) 𝟐 𝟑 𝟑 13) 1 14) Undef 15) 2 16) 3/4 17) 12/13 18) 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

Graphical Solutions of Trig Functions Section 8.1 Pre-Calculus AB PreAP/Dual, Revised ©2014 viet.dang@humble.k12.tx.us 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

Types of Trigonometric Functions Identities sin2x + cos2x = 1 1 + tan2x = sec2x 1 + cot2x = csc2x Conditional Equations Equations that are true for certain values sin x = 0 cos x = ½ 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Steps Put the equation into y= form In graphing calculator, it is necessary to change graphing windows Use 2nd trace 5, enter, enter, enter to find intersection points Round answers to 4 decimal places and add 2πk (sin, cos, sec, csc) or πk (cot, tan) Special Instructions: When the equation says sin2x, put in calculator as (sin x)2 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Example 1 Solve sin x = –0.75 from (0, 2π) 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Example 2 Solve cos x = 0.958 from (0, 2π) 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Example 3 Solve csc x = 1.45 from (0, 2π) 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Your Turn Solve sin x = 0.33 from (0, 2π) 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Example 4 Solve tan x – 3sin 2x = 0 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Example 5 Solve 3sin2 x = cos x + 2 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Your Turn Solve 4cos2 x + sin x – 2 = 0 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions

8.1: Graphical Solutions of Trig Functions Assignment Page 529 1-11 odd, 15-25 odd Go to dangmath.com to download a graphing calculator on the phone: http://www.dangmath.com/online-calculator.html 1/17/2019 6:03 AM 8.1: Graphical Solutions of Trig Functions