Solving 2nd degree Trig Equations
Solve for Ө such that 3600 coscos2 2
Substitute the trig function with xxx 22
Solve the quadratic equation02 2 xx
21
012 0
0)12(
x
xx
xx
Substitute x with the trig function21cos 0cos
Not done yet…
Where is cosine = 0
Where is cosine positive
21cos 0cos
60)(cos 211
Solve for Ө such that 3600 01coscos2 2
Substitute the trig function with x012 2 xx
Solve the quadratic equation
1
01 012
0)1)(12(
21
xx
xx
xx
Substitute x with the trig function1cos cos 21
Not done yet…
Where is cosine = -1
Where is cosine positive
21cos 1cos
60)(cos 211
Solve for Ө such that 3600 21tan2
Substitute the trig function with x212 x
Solve the quadratic equation32 x
3xSubstitute x with the trig function 3tan
60)3(tan 1
Solve for Ө such that 3600 0sin2sin 2
Substitute the trig function with x022 xx
Solve the quadratic equation0)2( xx
2 0 xx
Substitute x with the trig function2sin 0sin
errordomain )2(sin 1
Solve for Ө such that 3600 3tan5
tan
2
Substitute the trig function with x
352
xx Solve the quadratic: multiply both sides
by x to get rid of the denominator1
0)1)(25(
0235
352
52
2
2
x
xx
xx
xx
Substitute x with the trig function1tan tan 5
2
Now, substitute the trig function with x5
122
x
xSolve the quadratic: multiply both sides by x to get rid of the denominator
0)2)(12(
0252
5222
2
xx
xx
xx
You can’t substitute for x – there are two functions, not 1
But wait…csc is a reciprocal function!
sin
1csc
5sin
12sin2