This preview shows page 1. Sign up to view the full content.
Unformatted text preview: x ≈ 0.0300, 3.1716 19. (a) 36.87◦ and 53.13◦ (b) 22.62◦ and 67.38◦ 20. 68.9◦
24. (a) f (x) = 2 sin(x) − cos(x) = √ 5 sin(x + 5.8195) (b) g (x) = 5 sin(3x) + 12 cos(3x) = 13 sin(3x + 1.1760) (c) 32.52◦ and 57.48◦ 10.7 Trigonometric Equations and Inequalities 10.7 729 Trigonometric Equations and Inequalities In Sections 10.2, 10.3 and most recently 10.6, we solved some basic equations involving the trigonometric functions. In these cases, the equations were of the form T (x) = c where T (x) is some
circular function, x is a real number (or equivalently, an angle measuring x radians) and c is a real
number ostensibly in the range of T .1 We summarize how to solve these equations below.
Strategies for Solving Basic Equations Involving Trigonometric Functions
To solve equations of the form T (x) = c
• If T (x) = cos(x) or T (x) = sin(x), solve the equation for x on [0, 2π ) and add integer
multiples of the period 2π .
NOTE: If the arccos...
View Full Document