WorksheetsSteps to Solve Trig Equations
Total questions: 14
Worksheet time: 13mins
Which of these is equivalent to 2cos2x − 3cosx = 0 ?
-cos2x = 0
cosx(2cosx + 3) = 0
cosx(2cosx − 3) = 0
cos x = ⅔
Which is a correct way to solve the equation
cosx(2cosx − 3) = 0?
divide cos x from both sides
set each factor equal to 0 and solve
distribute cosx into the parentheses
guess and hope for the best
Why doesn't 2cosx − 3 = 0 have solutions?
cos x is never bigger than one
cos x is never equal to a fraction
Actually, this equation does have a solution, x = π
This equation will have a solution tomorrow.
Choose a good way to start solving this equation
tanx sin2x = 2 tanx
divide tanx from both sides
factor out tanx
subtract 2 tanx from the left and then factor tanx out
cancel sin2x out
So tanx sin2x = 2 tanx is equivalent to tanx(sin2x − 2) = 0
Then tanx = 0 or sin2x − 2 = 0, now what?
solutions come only from tanx = 0,
solutions come only from sin2x − 2 = 0
solutions come from where sin x is undefined
solutions come from where tan x is undefined
The square root of 2 is bigger than 1.
true
false
To solve this equation, cos2x + sinx = 1, replace cos2x with
1/(sec2x)
sin2x − 1
1 − sin2x
1 + tan2x
Organize this equation so it can be factored:
1−sin2x + sinx = 1
move all to the right: 0 = sin2x − sinx
cancel the ones and cancel a sinx
replace sin2x with 1 − cos2x
use this: 0 = sin2x − sinx + 2
Factor 0 = sin2x − sinx
0 = sinx(sinx)
0 = sinx(1 − sinx)
0 = cosx(sinx − 1)
0 = sinx(sinx − 1)
On the domain [0, 2π), solve this equation 0 = sinx(sinx − 1)
0, π
0, π, ½π
½π
0, 90, 270
csc2x = 2 is equivalent to sin2x = ½
True
False
To solve the equation sec2x − secx = 2
start by subtracting 2 from both sides and then factor
add sec x to both sides and factor
factor out secx and set each factor equal to 2
sec x is never bigger than 1, so there are no solutions
Factor: sec2x − secx − 2
(sec x)(secx − 2)
(secx − 2)(secx − 1)
(secx − 2)(secx + 1)
(secx + 2)(secx − 1)
Solve the equation (secx − 2)(secx + 1) = 0 on [0, 3600)
60⁰, 180⁰, 300⁰
30⁰, 180⁰,330⁰
60⁰, 120⁰
180⁰
