Trigonometry
What are the three trigonometric functions and their inverses?
Sine, cosine, tangent. Inverses (in order) are cosecant, secant, and cotangent.
Solve for x.
0=6x+3
x=-1/2
What are the 6 logic gates we discussed on Tuesday?
NOT, OR, AND, NOR, NAND, and XOR
/() = square root
Express /(-5) in terms of i.
5i
Who invented math?
No one!
What is the sine of the angle in a right triangle with an "opposite" of 7 meters and a "hypotenuse" of 13 meters?
7/13
Solve for x.
7=35x+9
x=-2/35
You feed an input of 1 and 0 into an AND logic gate. What is the output?
Simplify (1+2i)(3+i)
1+7i
How many thermal calories are in one food calorie?
1,000
What is the angle in a right triangle with an "adjacent" side measuring 3 inches and a "hypotenuse" measuring 4 inches?
41.4 degrees.
Factor the following polynomial.
y=x2+6x+9
y=(x+3)(x+3)
Suppose you have an AND gate (inputs A and B) parallel to an OR gate (inputs C and D), with an AND output receiving an output from the first two gates.
If A=B=C=D=1, what is the final output?
1
Simplify i^200
(i^2)^100 = 1
What are the 3 steps in an induction proof?
1). Prove the base case
2). Prove the formula is true for an arbitrary integer k
3). Prove the formula is true for k+1 relative to k
A right triangle has angle values of 90, 55, and 35 degrees. Suppose the hypotenuse has a value of 6 centimeters. What are the other two side lengths?
4.9 cm and 3.44 cm
Solve for x.
y=x2+13x+30
x=-3 and x=-10
x'=NOT x
Simplify the following: A'BC' + ABC'
BC'
What are the 3 forms of complex numbers called?
Cartesian, Polar, and Exponential
What civilization knew about trigonometry 3,700 years ago?
The Babylonians
You are setting up a tent and have driven three stakes into the ground, two of which form a right angle with the third. If the distance between the stake "touching" the right angle and the two other stakes are 3 meters and 4 meters respectively, what is the length of the hypotenuse and the value of the other two angles?
Hypotenuse: 5 meters
Angles: 53.13 and 36.87 degrees
y=3x3-6x2+9x
y=3x(x-3)(x-3)
x=0, x=3, x=3
Simplify the Following.
x'y'z + x'y'z' + xyz + x'y'z
x'y' + xyz
Convert 1+i to polar form.
/(2)(cos45 + isin45)
What two individuals are said to have invented calculus?
Isaac Newton and Gottfried Leibnitz