Reciprocal Identities
Pythgorean Identities
Negative Identities
Verifying Identities
Remember me?
100
csc x written as a reciprocal identity
1/sin x
100
This is the standard Pythagorean Identity.
(sinx)^2+(cosx)^2=1
100
cos(-x)=__________
cos(x)
100
Verify sinx/tanx=cosx.
sinx(cosx/sinx)=cosx
100
What is the period of y=Atan(Bx+C)?
Pi/B
200
sinxsecx simplies completely to ________
tan x
200
Prove that tan^2x+1=sec^2x.
Divide Pythagorean Identity sin^2x+cos^2x=1 by cos^2x.
200
csc(-x) = _________ (simplify using negative identities)
-csc(x)
200
Verify (1/cos^2x)-1=tan^2x.
Use reciprocal identity to get sec^2x-1 then use Pythagorean Identity.
200
Where does the graph of tan x have vertical asymptotes?
At k(pi) where k is an integer.
300
Simplify completely: secx/tanx
cscx
300
Simplify completely: [1-(cosx-sinx)^2]/(cosx)
2sinx
300
sec(-x)=________
secx
300
Daily Double!!! Verify (sec x)(sin x - cos x)=tan x -1
(1/cosx)(sinx-cosx)=(sinx/cosx)-(cosx/cosx)=tanx-1
300
Daily Double!! List the trig functions that have a period of 2pi.
sin x, cos x, csc x, sec x
400
Daily Double!! If cotx=-3/2 and cosx>0 find the exact values of the remaining trig functions.
tanx=-2/3, sinx=-2, cosx=3, cscx=-1/2, secx=1/3
400
Simplify (1/csc^2x)+(1/sec^2x).
1.
400
Daily Double!! sinx-([tan(-x)]/secx)
2sinx
400
Daily Double!!! Verify the identity: (1+cosx)/sinx + sinx/(1+cosx)=2cscx Hint: make a common denominator
;)
400
Find the phase shift and amplitude of y=5csc(4x-1).
Phase shift: 1/4, amplitude: DNE
500
If cosx=-4/5 and tanx=3/4 find the exact values of the remaining trig functions.
sinx=-3/5, cscx=-5/3, secx=-5/4, cotx=4/3
500
Show (sin^2x)/(1-cosx)=1+cosx Hint: use Difference of squares
Use Pythagorean Identity to rewrite sin^2x as 1-cos^2x, then use difference of squares.
500
Simplify cot(-x) completely.
cos(-x)/sin(-x)=cosx/(-sinx)=-cotx
500
Verify (1-cos^2x)/sin^3x=cscx
500
Find max and min of y=-13+4sin(2x).
Max:-9 Min:-17
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