Trigonometry, test 4

Domain of inverse sine

-1 is less than or equal to x is less than or equal to 1

Inverse function

A function has this if and only if for each domain element there is exactly one range element.

Mode

Before you solve for exact values, what part of the calculator should you switch to/check?

Inverse sine function

Defined as the inverse of the sine function restricted to -π/2 and π/2.

Inverse tangent

Defined as the inverse of the tangent function that has been restricted to (-π/2, π/2)

Vertical line test

Determines if you have a function.

0 and π

Exact value of cos^-1 x is between this and this.

-π/2 and π/2

Exact value of sin^-1 x is between this and this.

-π/2 and π/2

Exact value of tan^-1 x is between this and this.

Law of Sines

Follows the principle that (sin å)/a= (sin ß)/b = (sin ∂)/c

Law of cosines

Follows the principle that: a^2 = b^2 + c^2 -2bc coså b^2 = a^2 + c^2 -2accosß c^2 = a^2 + b^2 -2abcos∂

QI and IV for sine and tan, QI and II for cosine

Quadrants we focus on when dealing with inverses.

Horizontal line test

Tells you if the function is one-to-one.

Switch

What do the domains/ranges of inverse functions do?

Solve for the angle across from the biggest side

What do you do for a case 1 law of cosines problem?

Solve for the side across from the given angle, then solve for the angle that is across from the smaller of the two sides

What do you do for a case 2 law of cosines problem?

2π-(first solution)

What do you do to find the other solution in the other quadrant when solving for a trig equation?

+ 2πK, for KεZ

What do you write as the notation for "until infinity"?

That you want to find the angle whose sine is -1/3

What does it mean when you see something like tan(arccos -1/3)?

Quadratic formula

When finding exact values, what should you use if it doesn't factor?

Draw a triangle

When given an exact value, and you are expected to find the angle/real number, what do you have to do?

Radians

When it says, "For all real x", what format should the answer be in?

Innermost

When you have a parentheses inside of the parentheses, which do you take care of first: innermost or outermost?

Let w=θ/2, 2w=θ, distribute the w through, multiply the outcome by 2 when you are done

When you see something like cos(θ/2), what do you do?

Cosine identities

cos^-1(cos x)= x, for 0≤x≤π cos(cos^-1 x)=x, for -1≤x≤1

Sine identities

sin^-1 (sin x) = x, for -π/2≤x≤π/2 sin (sin^-1 x) = x, for -1≤x≤1

Tangent identities

tan^-1 (tan x)=x, for -π/2<x<π/2 tan x (tan^-1 x)=x, for -∞<x<∞