Section 7.5: Solving Trig Equations
January 09, 2015
2. tan2x - 1= 0
tan2x - 1= 0
Two ways to solve!
Directly
Factoring
3. 4cos2x - 1 = 0
Jan 11­7:54 AM
4. 2sin2x + sinx = 0
5. 4cos2x + 3cosx - 1= 0
Jan 11­7:55 AM
tan2x - 1= 0
Section 7.5: Solving Trig Equations
January 09, 2015
Solve with using trig identities to help you.
Remember
sin2 x + cos2 x = 1, thus...
sin2 x = 1 - cos2 x
cos2 x = 1 - sin2 x
Jan 11­7:57 AM
6. cos2x - sinx + 1 = 0
Jan 11­7:59 AM
Section 7.5: Solving Trig Equations
January 09, 2015
7. 3sin2x + cosx + 1 = 0
Jan 11­8:00 AM
Day 2: Double Angle Identities & Erroneous Solutions
2x ≠ x
sin2x = 2sinxcosx
to solve an
equation you must
be using the same
angle in each trig
function
cos2x = cos2 x - sin2 x
= 2cos2 x -1
= 1 - 2sin2 x
1.) 6sin2x = 6cosx
Jan 10­7:33 AM
Section 7.5: Solving Trig Equations
January 09, 2015
2. cos2x + 8sin2 x + sinx = 3
Jan 10­7:34 AM
3. cos2x + 6cos 2 x + 2cosx = 2
Jan 10­7:34 AM
Section 7.5: Solving Trig Equations
January 09, 2015
Erroneous Solutions - solutions you get while solving that do not
work in the original problem
*only occurs when there is a tangent or cotangent & a quadrant
angle, because the functions could be undefined at those points.
*the same would be true for sec & csc at their points of
discontinuity
4. sinxtanx - tanx = 0
Jan 10­7:34 AM
5. 3sinxcotx - 4sinx = 0
Jan 10­7:35 AM