SohCahToa
Unit Circle
Rational Functions
Simplify
Composite Functions
100
What is the length of K?
The length of K is 74.77
100
Find the exact value: sin 315° =
-sqrt2/2
100
What are the roots and vertical asymptotes of the function:
1/(x^2+2x-3)
Roots: Undefined
Vertical Asymptotes: x= -3, x= 1
100
Simplify the following:
-2/sqrt3
-(2sqrt3)/3
100
If
f(x)=x^2+3, What is f(-6)?
f(-6)= 39
200
What is the measure of the red angle?
The measure of the red angle is 36.9 degrees
200
Find the exact trig value: tan 5π/3 =
-sqrt3
200
What is the y-intercept of the function
(2x^2-16x+30)/(x^2-x-12)
Y intercept:
(0, -5/2)
200
Simplify the following:
6/(3sqrt5)
(2sqrt5)/5
200
Assume the following. Find f(g(-1))
f(x)=2x-1 and g(x)=-3x+2
f(g(-1))=9
300
What is the ratio of tan theta?
(2sqrt5)/5
300
Find the exact trig value: sin -120° =
-sqrt3/2
300
Where are the zeros of this function
(3x+6)/(x^2-8x+16)
Zeros at 3x+6=0, so at (-2, 0)
300
Simplify the following:
(x^2-9x-14)/(x^2+2x-8)
(x-7)/(x+4)
300
Assume the following. Find f(g(x))
f(x)=x^2 and g(x)=sqrtx
f(g(x))=x
400
The tallest television transmitting tower in the world is in North Dakota, and is 2059 feet tall. If you are on ground level exactly 5280 feet (1 mile) from the base of the tower, what is your angle of elevation?
Your angle of elevation is 21 degrees
400
Find the exact trig value: cos 1140° =
(same as cos 60°)
1/2
400
What are the roots and vertical asymptotes of this function?
(x^2+3x-10)/(3x^2-3x-6)
Roots: (-5, 0)
Vertical Asymptotes: x=-1
400
Simplify the following:
(x^2-2)^2-11
x^4-4x^2-7
400
Assume the following. Find f(f(x))
f(x)=x^2+3
f(f(x))=x^4+6x^2+12
500
Two ladders are leaning against a building, as shown. What is the angle of elevation of the shorter ladder?
The angle of elevation is about 57 degrees.
500
In which quadrant(s) would cotangent be negative?
Quadrants 2 and 4
500
Sketch a graph of this function:
(2x^2-16x+30)/(x^2-x-12)
500
Simplify the following:
(2x^4+9x^3-5x^2)/(6x^3+x^2-2x)
(x(x+5))/(3x+2)
500
Assume the following. Find g(f(-2))
f(x)=x^3+2x and g(x)=x-9
g(f(-2))=-21