Exam 1
Find the x-y intercepts of the graph of the equation x2-xy+5y=9
x:(0,9/5)
y: (3,0), (-3,0)
Express f(x) = x2+6x-83 in Standard (Vertex) form
What's the max/min point?
f(x) = (x+3)2-92
Min (-3,-92)
Convert to radian
315°
(7pi/4)
To define the tangent function, we restrict the domain of tangent to the interval ____
[-π /2, π/2]
Without calculator, calculate:
sin18°cos27° +cos18°sin27°
= sin(18°+27°) = sin(45°) = √2/2
Inverse Function of
f(x)=(4+sqrtx)^3
f^-1(x)=(3sqrtx-4)^2
Vertical + Horizontal asymptote of r(x)
x=-2, x=3
y=1
A ramp is 17 ft long with a 62° angle of elevation. When a rider gets to the top of ramp for a jump, what height does the rider reach?
sin 62° =x/17
Simplify
cos(t)tan(t)
cos(t)*sin(t)/cos(t)=sin(t)
Simplify
sin8°/(1+cos8°)
=tan((8°)/2)=tan(4°)
Find an equation of the circle that satisfies the given conditions:
Center (-3,7); tangent to the y-axis
(x+3)2+(y-7)2=9
If $30,000 is invested at an interest rate of 3.5% per year compounded continuously, find the value of the investment at the end of 7 years.
A = Pe^(rt) = 30,000*e^(0.035*7)=38,133.07
Find the value using the unit circle
tan ((7pi)/4)=
tan ((7pi)/4)=-1
cos^-1(cosx))=x
0 <= x <= π
Evaluate without a calculator
(tan(9pi/12)-tan(5pi/12))/(1+tan9pi/12*tan5pi/12)
tan(9pi/12-5pi/12)=tan(4pi/12)=tan(pi/3)=sqrt3
The graphs of f and g are given, find a formula for the function g
g(x) = -(x-3)^2+1
A bag of frozen bananas is thrown upwards ... You know the drill
H(t) = -16t2+48t+32
What's the maximum height? When does it happen?
max height = 68 (ft)
t = 1.5 (s)
ln(e^x^2)*10^log(4x^5)
4x7
Simplify
sin(theta)/(1+cos(theta))+(1+cos(theta))/sin(theta)
=(sin^2theta+(1+costheta)^2)/((sintheta(i+costheta))
=(1+1+2costheta)/sintheta(i+costheta)=2/sintheta
=2csctheta
P is a point on the unit circle in quadrant IV. Fill in the blank with the missing coordinate
P(__,-7/25)
P(24/25,-7/25)
Formula for a piecewise function
f(x) = 4, if -5 <= x <= -1
f(x) = -x+4, if -1 < x <=2
f(x) = 1, if x > 2
(-22/7,11)
Find the reference angle for -410°
50°
Simplify the trigonometric expression
cosx/(secx+tanx)
cosx/(1/cosx+sin/cosx) = cosx/((1+sinx)/cosx)
= cos^2x/(1+sinx) = (1-sin^2x)/1+sinx
=((1-sinx)(1+sinx))/(1+sinx)
=1-sinx
Simplify the following expression
sin^-1(sin(7pi/6))
-pi/6