academy algebra ii/trig pre-calculus (5.1, 5.2) 8.3: trigonometric identities hw: today: none,...
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Academy Algebra Academy Algebra II/TrigII/Trig
Pre-Calculus (5.1, 5.2)Pre-Calculus (5.1, 5.2)
8.3: Trigonometric IdentitiesHW: today: none,
Tomorrow: p.625-626 (20, 24, 32, 38, 50, 54, 78, 86)
Quiz 8.3 (PC 5.1-5.2): Monday, May 19th
(Bio-Testing: 20th and 21st)
Trig IdentitiesTrig Identities• Reciprocal Identities
• Quotient Identities
uu
uu
uu
uu
uu
uu
tan
1cot
cos
1sec
sin
1csc
cot
1tan
sec
1cos
csc
1sin
u
uu
u
uu
sin
coscot
cos
sintan
Trig IdentitiesTrig Identities• Pythagorean Identities
• Even/Odd Identities
uu
uu
uu
22
22
22
csccot1
sectan1
1cossin
uuuu
uuuu
uuuu
cot)cot( tan)tan(
sec)sec( cos)cos(
csc)csc( sin)sin(
Trig IdentitiesTrig Identities• Cofunction Identities (section 7.6)
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uuuu
uuuu
sec2
csc csc2
sec
tan2
cot cot2
tan
sin2
cos cos2
sin
Simplify the Trig ExpressionSimplify the Trig ExpressionP.381 (#22)
))(secsin1( 2 xxCheck using your calculator:Y1= Question
Y2= Answer
Check: graphs/tables are the same
5.2: Verifying Trig Identities5.2: Verifying Trig Identities1.) Work with one side of the equation.2.) Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator.3.) Look for opportunities to use the fundamental identities.4.) If the preceding guidelines do not help, try converting to all sines and cosines.5.) Try something! Even making an attempt that leads to a dead end gives insight.