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