Solving Trigonometric

Identities

Classify the following

A – an expression to simplify

C – an equation that is sometime true

B – an equation that is never true

D – an equation that is always true – an identity

C

A

D

B

1,0 1,0

0,1

0, 1

cos ,sinx x

0 2

2

3

2

4

2 2,

2 2

3

4

2 2,

2 2

5

4

2 2,

2 2

7

4

2 2,

2 2

6

3 1,

2 2

3

1 3,2 2

2

3

1 3,

2 2

5

6

3 1,

2 2

7

6

3 1,

2 2

4

3

1 3,

2 2

5

3

1 3,2 2

11

6

3 1,

2 2

00

3

33

3

3

3

3

3

1

1

1

1

33

33

tan x

und

und

2

06

4

3

2

Cosine are the fingers left on top

Sine are the fingers left on bottom

Whatever angle you are dealing with, pull that finger back in.

Solve algebraicallyUse inverse operations to solve each equation on the interval 0,2

2sin 1x tan 1 0x

Solve algebraicallyUse inverse operations to solve each equation on the interval 0,2

4cos 1 3x 22cos 1 0x

Simplify and SolveSimplify each side of the equation, then solve on the interval 0,2

sin cot 0x x cos tan csc 1x x x

Sometimes, when multiplying or dividing by an expression on both sides of an equation, extraneous solutions can be introduced. Be sure to check your final solutions.

Simplify and SolveSimplify each side of the equation, then solve on the interval 0,2

2cos tan sin csc 0x x x x

Simplify and SolveSimplify each side of the equation, then solve on the interval 0,2

cos tan sin csc 0x x x x

Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2

Solving tips:• Always look for a common factor first.• If no common factor is present, you may have to use an identity

to rewrite the expression in terms of one function – using the same trig function or argument.

• Then you can factor into two parentheses.

Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2

tan sec tanx x x

Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2

24cos 1 0x

Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2

2cos 3sin 3 0x x

Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2

2sec 2 tan 4x x

5.3 p. 396 8-40 evens54-62 evens