Trig Concepts
What are the reciprocal Identities?
Cosecant, secant, cotangent
Which double angle formula has 3 equivalent identities?
cos(2x)
Graphically, how do you prove identities?
Graph both sides and see if they perfectly match
Which quadrant does the CAST rule begin with?
4th Quadrant
sin(a+b)=
sinacosb+cosasinb
Solve: Cotx + tanx = secx cscx
Show all work
LS = cosx/sinx + sinx/cosx
=((cosx)^2 + (sinx)^2)/ sinx cosx
= 1/ sinx cosx
= (1/sinx) (1/cosx)
=secx cscx =RS QED
What quadrant is cos 7pi/10 in?
2nd Quadrant.
cos(a-b)=
cosacosb+sinasinb
Evaluate sin(-Pi/12) using a compound angle formula
=sin(Pi/4-Pi/3)
=sin(Pi/4)cos(Pi/3)-cos(Pi/4)sin(Pi/3)
=(1/sqrt(2))(1/2)-(sqrt(3)/2)(1/sqrt(2))
=(1-sqrt(3))/2sqrt(2)
Given that cos Pi/5 = 0.809, use equivalent trig identities to find sin(17pi/10) Which identity would you use?
3pi/2 + x
What is the Pythagorean identity?
(sinx)^2+(cosx)^2=1
Solve (sinx)^2=1/2 over xE[0,2pi]
x=api/4 aE{1,3,5,7}
What axis are the co-related identities derived from? (ex. Pi/2+x)
The y-axis
What is the double angle formula for tan(2x)?
(2tanx)/(1+(tanx)^2)
Solve: (secx)^2 - (secy)^2 = (tanx)^2 - (tany)^2
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RS = (tanx)^2 - (tany)^2
= ((secx)^2 - 1) - ((secy)^2 - 1)
= (secx)^2 - 1 + 1 - (secy)^2
= (secx)^2 - (secy)^2 = LS QED