Terminal Points
Trigonometric Functions
Even/Odd Properties & Identities
Trigonometric Graphs
100
Find the y-coordinate of P(-3/5,y) if P lies on the 3rd quadrant of the unit circle.
y=-4/5
100
Evaluate sint , cost, and tant determined by t=pi/2 .
sin(pi/2)=1
cos(pi/2)=0
tan(pi/2)= undefined
100
Find the relationship between a) sin(-pi/6) and sin(pi/6) , b) cos(-pi/4) and cos(pi/4) and c) tan(-pi/3) and tan(pi/3)
sin(-pi/6)=-sin(pi/6)
cos(-pi/4)=cos(pi/4)
tan(-pi/3)=-tan(pi/3)
100
Find the period and the phase shift of y=-tan2(x+pi/4).
p=pi/2 and it is shifted pi/4
units to the left.
200
Find the terminal point P(x,y) on the unit circle determined by t=-3pi .
P(-1,0)
200
Evaluate sint , cost, and tant when the terminal point determined by t is P(3/5,-4/5) .
sint=-4/5
cost=3/5
tant=-4/3
200
Determine whether f(x)=tanx * sinx is even, odd, or neither.
Even
200
Find the range of f(x)=2/3sin(3x) .
[-2/3,2/3]
300
Find the terminal point P(x,y) on the unit circle determined by t=(7pi)/4 .
P(sqrt2/2,-sqrt2/2)
300
Evaluate sint , cost, and tant determined by t=-(3pi)/4 .
sin(-(3pi)/4)=-sqrt2/2
cos(-(3pi)/4)=-sqrt2/2
tan(-(3pi)/4)=1
300
If cost=-4/5 and t is in Quadrant III, find sint and tant.
sint=-3/5
tant=3/4
300
Find the amplitude, period, and phase shift of y=3cos(pix-pi/2).
|a|=3, p=2, and it is shifted 1/2 units to the right.
400
Find the terminal point P(x,y) on the unit circle determined by t=-(11pi)/3 .
P(1/2,sqrt3/2)
400
Evaluate sint , cost, and tant determined by t=(73pi)/6 .
sin((73pi)/6)=1/2
cos((73pi)/6)=sqrt3/2
tan((73pi)/6)=sqrt3/3
400
Determine whether f(x)=(sin^3x*cosx)/(x*tan^5x) is even, odd, or neither.
Odd
400
Find the amplitude, period, and phase shift of y=2sec(4x+pi/3).
|a|=2, p=pi/2, and it is shifted pi/12 units to the left.
500
Find the terminal point P(x,y) on the unit circle determined by t=(29pi)/6 .
P(-sqrt3/2,1/2)
500
Evaluate sint , cost, tant, csct, sect, and cott, determined by t=(2pi)/3 .
sin((2pi)/3)=sqrt3/2
cos((2pi)/3)=-1/2
tan((2pi)/3)=-sqrt3
csc((2pi)/3)=(2sqrt3)/3
sec((2pi)/3)=-2
cot((2pi)/3)=-sqrt3/3
500
If tant=5/12 and cost>0, find sint and cost.
cost=12/13
sint=5/13
500
Write an equation that represents the function in the form y=acos(b(x+c))+d .
y=-3cos(2x)-1