http://www.ck12.org Chapter 6. Analytic Trigonometry
6.1 Basic Trigonometric Identities
Here you will simplify trigonometric expressions using the reciprocal, quotient, odd-even and cofunction identi-
ties. You will also apply these simplification techniques in trigonometric proofs.
The basic trigonometric identities are ones that can be logically deduced from the definitions and graphs of the six
trigonometric functions. Previously, some of these identities have been used in a casual way, but now they will be
formalized and added to the toolbox of trigonometric identities.
How can you use the trigonometric identities to simplify the following expression?
[sin
(π 2 −θ)
sin(−θ)
]− 1
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61313http://www.youtube.com/watch?v=_gkuml–4_Q James Sousa: Cofunction Identities
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61315http://www.youtube.com/watch?v=YbU8Sq0quWE James Sousa: Even and Odd Trigonometric Identities
Guidance
The reciprocal identities refer to the connections between the trigonometric functions like sine and cosecant. Sine is
opposite over hypotenuse and cosecant is hypotenuse over opposite. This logic produces the following six identities.
- sinθ=csc^1 θ
- cosθ=sec^1 θ
- tanθ=cot^1 θ
- cotθ=tan^1 θ
- secθ=cos^1 θ
- cscθ=sin^1 θ