Solving Trigonometric Equations
But first - is there anything you want me
to prove?
p. 540 # 11b) sin2x + cos4x = cos2x + sin4x
LS = sin2x + cos4x
=sin2x + (cos2x)2
=sin2x + (1 - sin2x)2
first pyth identity
Trig. Test #2
May 13
10
ay
=sin2x + (1 - sin2x) (1 - sin2x)
=sin2x + 1 - 2sin2x + sin4x
2
4
LS=RS
M
st al
e
t
n
Re atio ons
R
i
on ress
p
ex
= 1 - sin x + sin x
= cos2x + sin4x
is there anything
else
you want me to prove?
Solving equations.
Solve for x
2sinx+1=0,
0≤x≤360o
2sinx = -1
sinx = -½
Solve for x
2cosx-√3=0,
-2π≤x≤0
solve for B,
3sinB-2=0,
0<B<360o
3sinB = 2
sinB =
B= sin-1(
)
o
B = 41.81
B=180o - 41.81o
= 138.19o
These three examples were
LINEAR trig equations since
nothing was squared or
cubed....
Quadratic Trigonometric Equations (connects quadratics and trig.)
Solve for x.
2cos2x - 7cosx + 3 = 0
2A2-7A+3=0
(2A - 1)(A - 3)=0
(2cosx - 1)(cosx - 3)=0
Cosx = 1/2
cosx = 3
A = 1/2
A=3
Solve for x, 0≤x≤2π
2sin2x+3sinx+1=0
(2sinx + 1)(sinx +1)=0
sinx = -1/2
sin x = -1
Solve for x, 0≤x≤2π
2
sin x - 6 sinx - 1 =0
2A2+3A+1=0
(2A+1)(A+1)=0
A=-1/2, A=-1
A2- 6 A - 1 = 0
Neither linear nor quadratic
2sinx+3sinxcosx=0
common factor out sinx
sinx ( 2 + 3cosx ) =0
0<x<360o