Trig Identities Jeopardy

Reciprocal Identities

100

csc x written as a reciprocal identity

1/sin x

200

sinxsecx simplies completely to ________

tan x

300

Simplify completely: secx/tanx

cscx

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

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

Pythgorean Identities

100

This is the standard Pythagorean Identity.

(sinx)^2+(cosx)^2=1

200

Prove that tan^2x+1=sec^2x.

Divide Pythagorean Identity sin^2x+cos^2x=1 by cos^2x.

300

Simplify completely: [1-(cosx-sinx)^2]/(cosx)

2sinx

400

Simplify (1/csc^2x)+(1/sec^2x).

1.

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.

Negative Identities

100

cos(-x)=__________

cos(x)

200

csc(-x) = _________ (simplify using negative identities)

-csc(x)

300

sec(-x)=________

secx

400

Daily Double!! sinx-([tan(-x)]/secx)

2sinx

500

Simplify cot(-x) completely.

cos(-x)/sin(-x)=cosx/(-sinx)=-cotx

Verifying Identities

100

Verify sinx/tanx=cosx.

sinx(cosx/sinx)=cosx

200

Verify (1/cos^2x)-1=tan^2x.

Use reciprocal identity to get sec^2x-1 then use Pythagorean Identity.

300

Daily Double!!! Verify (sec x)(sin x - cos x)=tan x -1

(1/cosx)(sinx-cosx)=(sinx/cosx)-(cosx/cosx)=tanx-1

400

Daily Double!!! Verify the identity: (1+cosx)/sinx + sinx/(1+cosx)=2cscx Hint: make a common denominator

;)

500

Verify (1-cos^2x)/sin^3x=cscx

Remember me?

100

What is the period of y=Atan(Bx+C)?

Pi/B

200

Where does the graph of tan x have vertical asymptotes?

At k(pi) where k is an integer.

300

Daily Double!! List the trig functions that have a period of 2pi.

sin x, cos x, csc x, sec x

400

Find the phase shift and amplitude of y=5csc(4x-1).

Phase shift: 1/4, amplitude: DNE

500

Find max and min of y=-13+4sin(2x).

Max:-9 Min:-17