January 15, 2010
Basic Trigonometric Identities
Pythagorean Identities
Example Using Identities
Cofunction Identities
January 15, 2010
Cofunction Identities
Even-Odd Identities
Example Simplifying by Factoring and Using
Identities
Example Simplifying by Expanding and Using
Identities
Example Solving a Trigonometric Equation
Examples:
Find secθ and cscθ if tanθ=3 and cosθ >0
January 15, 2010
Examples:
Use basic identities to simplify the expression.
1+ tan2θ
---------------csc2θ
cotθ tanθ
Simplify the expression to
either 1 or -1
secθ csc(-x)
sin2θ + tan2θ + cos2θ
---------------------------------------secθ
Simplify the expression to either a constant or a basic
trigonometric function.
Use the basic identities to change the expression to
one involving only sines and cosines. Then simplify to a
basic trigonometric function.
(sec2θ + csc2θ) - (tan2θ + cot2θ)
sinθ -tanθcosθ + cos(π/2 -θ)
tanθ + tanθ
csc2θ
sec2θ
Combine the fractions and simplify to a multiple of a
power of a basic trigonometric function.
Write each expression in factored form as an
algebraic expression of a single trigonometric funtion.
_1___ + _1___
1- sinx
1+ sinx
1 - 2sinx + (1-cos2x)
secx - sinx
sinx
cosx
sin2x
1+cosx
January 15, 2010
Find all solutions to the equation in the interval [0,
2π]. You do not need a calculator.
√2tanx·cosx - tanx = 0
2sin2x = 1
Homework:
page 451:
3-72 multiples of 3, skip 6