PreCalculus

Find the inverse

100

Find the inverse of f (x)=4√x

f^-1(x)=x^4 for x≥0

200

Find the inverse of this function.

h(x)=3/-x -2

There isn't one

300

State if the given functions are inverses

g(x)=-4x

f(x)=-6x-1

No

400

Find the inverse of each function.

h(x)=-2x=5

h^-1(x)=-1/2x+5/2

500

State if the given functions are inverses.

g(n)=4/-n+2

f(n)=-4/n+2

Yes

Math history

100

What year is trigonometry taught?

In general, trigonometry is taken as part of sophomore or junior year math. In addition to being offered as its own course, trigonometry is often incorporated as a unit or semester focus in other math courses.

200

What is trigonometry mostly about?

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

300

Who actually invented trigonometry?

This makes Hipparchus the founder of trigonometry. The next Greek mathematician to produce a table of chords was Menelaus in about 100 AD. Menelaus worked in Rome producing six books of tables of chords which have been lost but his work on spherics has survived and is the earliest known work on spherical trigonometry.

400

When was pre calc invented?

Leonhard Euler wrote the first precalculus book in 1748 called Introductio in analysin infinitorum (Latin: Introduction to the Analysis of the Infinite), which "was meant as a survey of concepts and methods in analysis and analytic geometry preliminary to the study of differential and integral calculus.

500

Which Decades were considered "the precalculus period"?

The decades between 1610 and 1670, referred to in the history of mathematics as “the precalculus period,” were a time of remarkable activity in which researchers throughout Europe contributed novel solutions and competed with each other to arrive at important new methods.

Inverses

100

What is the inverse of cosine?

arccos

200

What is the inverse of tangent?

arctan

300

What is the inverse of sin?

arcsin x

400

How do you find the inverse of a function?

Switch the x and y and then solve for y.

500

Find the inverse of f(x)=3x-4.

f^-1 (x)=x/3+4/3

Calculate This

100

arccos(-1/2)

0

200

arctan(1)

pi/4

300

arctan(0)

0

400

arccos(-1)

pi

500

arcsin(0)

pi/2

x=

100

-3 + 2x = 11

x = 7

200

2x + 6 = 4x - 2

x = 4

300

2x - 10 = 10 - 3x

x = 4

400

-10x - 19 = 19 - 8x

x = -19 

500

 17x - 12 = 114 + 3x

x = 9