6.1. Basic Trigonometric Identities http://www.ck12.org
tanθ=o p pad j=(o p p
hy p)
(ad j
hy p)
=cossinθθ- As Example C and Example A show, cos(θ−π 2 )=cos(π 2 −θ).
0. 68 =cos(
θ−π 2)
=cos(π
2 −θ)
=sin(θ)Then, csc(−θ) =−cscθ
=−sin^1 θ
=−( 0. 68 )−^1cosxsinxtanxcotxsecxcscx=cosxsinxtanx·tan^1 x·cos^1 x·sin^1 x
= 1Practice
- Prove the quotient identity for cotangent using sine and cosine.
- Explain why cos(π 2 −θ)=sinθusing graphs and transformations.
- Explain why secθ=cos^1 θ.
- Prove that tanθ·cotθ=1.
- Prove that sinθ·cscθ=1.
- Prove that sinθ·secθ=tanθ.
- Prove that cosθ·cscθ=cotθ.
- If sinθ= 0 .81, what is sin(−θ)?
- If cosθ= 0 .5, what is cos(−θ)?
- If cosθ= 0 .25, what is sec(−θ)?
- If cscθ= 0 .7, what is sin(−θ)?
- How can you tell from a graph if a function is even or odd?
- Provetancscx·secxx·cotx=tanx.