4.3 Solving The Most Complex Trigonometric Equations


In this section,
We will be taking a look at the most complex equations. When solving the most complex trig equations, it is important to make sure the equation cannot be simplified. one way you could simplify a trig equation is by factoring and using the zero product property. Take a look:
Solving these equations:
- Simplify the equation
- Determine if the equation can be factored
- Use the zero product property
Examples:
Ex.1
3 Tan2x + 5Tanx = 0
Tanx (3Tanx + 5) = 0 ←Factor out GCF
Tanx = 0 Tanx = -5/3 ←Set equal to 0
X=0,π Tanx-1=-5/3
Quadrants: II, IV ←Find quadrants
X1=1.03
II = 2.11
IV = 5.25
Solutions: {2.11, 5.25}
Ex.2
6sin2x + 7sinx - 5 = 0
(3sinx + 5) (2sinx - 1) = 0 ←Factor
3sinx + 5 = 0 2sinx - 1 = 0 ←Set equal to 0
sinx = -5/3 sinx = ½
Quadrants: I, II ← Find quadrants
XI = π/6
I = π/6
II = 5π/6
Solutions: {π/6, 5π/6}
Practice Problems:
ANSWER KEY
1) Tan2x + 2tanx = -1
2) 2sin2x - 3 sinx + 1 = 0