Unit 7 Solving TRIG Equations Form B

f(x)=cos(x) + sin(x)

f(x) = 2sin(x+5) - 3

f(x) = cos(x)sin(x) + sin(x)cos(x)

f(x) = 3cotan(x) + 2

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

1

2

3

4

TRIG functions will always have 2 solutions.

Sin and Cos will have 2 solutions. Tan will have 1 solution.

All TRIG functions have an infinite number of solutions unless the domain is restricted.

The TRIG function will have 0, 1, or 2 solutions.

0

0

1

2

-1

-2

2sin(x) - 1

csc(x)-tan(x)

0

-1

cos(x) - 2sin(x)

divide by cosine

divide by sine

multiply by sine

apply the arccos function

apply the arcsin function

an equation of a functions that results in a solution of 1. These identities are fundamental tools for simplifying expressions, solving equations, and proving other trigonometric relationships.

an equation involving trigonometric functions that remains true for sine, cosine, and tangent values of the variable within the domain of the functions. They are not always true for csc, sec, and cot.

an equation involving trigonometric functions that remains true for all values of the variable within the domain of the functions. These identities are fundamental tools for simplifying expressions, solving equations, and proving other trigonometric relationships.

an equation of a function that results in both sides being equal. These identities are fundamental tools for simplifying expressions, solving equations, and proving other trigonometric relationships.

y=sin(x-4)

y=sin(x+4)

y=sin(x) + 4

y=sin(x) +8

y = -10sinx

y = 4sinx + 100

y = -6sinx - 20

y = 2sin(x+50)

y = 2cos(12x)

y = sin(x/30)

y = cos(10x)

y = 7sin(3x - 50)

Rewrite everything in terms of sine and secant.

Rewrite everything in terms of cosecant and secant.

Start cancelling things out.

Rewrite everything in terms of sine and cosine.

The right triangle

The right square

The unit circle

The Pythagorean Theorem

1/cosine

1/cosecant

1/secant

1/cotangent

1/2

-1/2

1

-1

-1

26

36

23