Amplitude & Period
What is the amplitude of this function?
y=3sinx
The amplitude is:
3
Describe the shift(s) in the following:
y=4sin(x-pi)
Right
pi
What is the reciprocal of sine?
Cosecant!
Find the exact value of cosecant given the following:
sinx=3/5
5/3
(Verbal Response)
Half the distance between the top and bottom
What is the period of this function?
y=sin(2x)
The period is:
pi
Describe the shift(s) in the following:
y=-8cos(x)+9
Up
9
What is the Pythagorean Identity that uses sine and cosine?
sin^2x+cos^2x=1
Use the sine sum identity to derive the identity for:
sin(2x)
sin(2x)=2sin(x)cos(x)
Define Period
(Verbal Response)
The distance over which one full cycle of a wave takes place.
Find the value of b for a tangent function with the following period:
4pi
the value of b is:
1/4
Write the equation of sine with only the following transformations:
Right by:
pi/3
Down by:
2
y=sin(x-pi/3)-2
Fully simplify the following expression:
(cos^3theta+sin^2thetacostheta)/cottheta
csctheta
Find sin(A+B) using the following:
cosA=12/13
tanB=3/4
56/65
Define Reciprocal
(Verbal Response)
The "flipped" fraction of a value or function
Use the following function to determine the amplitude and period:
y=-2cos(3x)
The amplitude is:
2
And the period is:
(2pi)/3
Write the equation of tangent with only the following transformations:
Left by:
(3pi)/4
Up by:
e
y=tan(x+(3pi)/4)+e
Describe how to go from the sine and cosine Pythagorean ID to the ones involving tangent and cotangent
(Verbal Response)
To arrive at the secant/tangent ID - we divide each term in the original by cosine squared.
To arrive at the cosecant/cotangent ID - we divide each term in the original by sine squared.
Using the sum and difference IDs find the following:
sin(pi/4+pi/3)
(sqrt2+sqrt6)/4
Where would we find Asymptotes when graphing tangent?
(Verbal Response)
Input values where the cosine function outputs 0
Use the following function to determine the amplitude and period:
y=tanx
There is no amplitude, and the period is:
pi
Explain how to determine the shifts in a given trig function
(Verbal Response)
adding or subtracting on the argument (inside) shifts left and right respectively
adding or subtracting to the function (outside) shifts up and down respectively
Fully simplify the following:
((1-sintheta)(1+sintheta))/costheta*sectheta
1
If tan(x)=1, find tan(2x)
Hint: What angle has the same sine and cosine value?
The angle would be
pi/2
This means cos(x)=0, so...
tan(2x) is undefined
State the midline equation for the following function:
y=6cot(x-96pi)-2
y=-2