Solving Trigonometric Equations
Solving Trigonometric Equations (page 1 of 2) Solving trig equations use both the reference angles you've memorized and a lot of the algebra you've learned. Be prepared to need to think! Solve sin(x) + 2 = 3 for 0° < x < 360° Just as with linear equations, I'll first isolate the variable-containing term: sin(x) + 2 = 3 sin(x) = 1 Now I'll use the reference angles I've memorized: x = 90° Solve tan2(x) + 3 = 0 for 0° < x < 360° There's the temptation to quickly recall that the tangent of 60° involves the square root of 3 and slap down an answer, but this equation doesn't actually have a solution: tan2(x) = –3 How can the square of a trig function evaluate to a negative number? no solution Solve on 0° < x < 360° To solve this, I need to do some simple factoring: Now that I've done the algebra, I can do the trig. x = 30°, 90°, 270°, 330° Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved Solve sin2(x) – sin(x) = 2 on 0° < x < 360° Only one of the factor solutions is sensible. x = 270° Hmm...
Related: Collection 1: MA301 Trigonometric Functions