a – an expression to simplify c – an equation that is sometime true b – an equation that is...
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Solving Trigonometric
Identities
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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
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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
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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.
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Solve algebraicallyUse inverse operations to solve each equation on the interval 0,2
2sin 1x tan 1 0x
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Solve algebraicallyUse inverse operations to solve each equation on the interval 0,2
4cos 1 3x 22cos 1 0x
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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.
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Simplify and SolveSimplify each side of the equation, then solve on the interval 0,2
2cos tan sin csc 0x x x x
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Simplify and SolveSimplify each side of the equation, then solve on the interval 0,2
cos tan sin csc 0x x x x
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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.
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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
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Factor and solveSet one side of the equation equal to zero; then factor to solve on the interval 0,2
24cos 1 0x
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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
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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
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5.3 p. 396 8-40 evens54-62 evens