III

225^o

-√2, -√2

   2     2

5∏

4

IV

315^o

√2, √2

 2     2

7∏

4

II

135^o

-√2, √2

  2     2

3∏

4

I

45^o

√2, √2

 2     2

∏

4

IV

300^o

1, -√3

2    2

5∏

3

III

210^o

-√3 , -1

   2     2

7∏

6

II

120^o

-1, √3

 2    2

2∏

3

I

60^o

1, √3

2    2

∏

3

IV

330^o

√3, -1

 2     2

11∏

6

III

240^o

-1, -√3

 2     2

4∏

3

II

150^o

-√3, 1

   2   2

5∏

6

I

30^o

√3, 1

 2   2

∏

6

180^o

(-1,0)

∏

0^o

(1,0)

0

270^o

(0,-1)

3∏

2

90^o

(0,1)

∏

2

What are the exact values of the acute angles?

[image]

Answer: 1, 1, hypotenuse = √2

What are the exact values of the sides and the hypotenuse?

[image]

Answer: 45^o and 45^o

What are the exact values of the sides and the hypotenuse?

[image]

Answer: 30^o, 60^o

What are the exact vlaues of the acute angles?

2 [image]√3

1

Answer: 1, √3, hypotenuse=2

SIN

(Acute Angles)

   Opposite   

Hypotenuse

SIN

(Any Angles)

y

r

SIN

(Real Numbers)

y

COS

(Acute Angles)

  Adjacent  

Hypotenuse

COS

(Any Angle)

x

r

COS

(Real Numbers)

X

TAN

(Acute Angles)

Opposite

Adjacent

TAN

(Any Angle)

y

x

TAN

(Real Numbers)

y

x

Quadrant

IV

(positive, negative)

Quadrant

III

(negative, negative)

Quadrant

II

(negative, positive)

Quadrant

I

(positive, positive)

Trig Function Pattern

(Real Numbers)

hint: circles

y         x       y/x

1/y     1/x     x/y

Trig Function Pattern

(Acute Angles)

hint: triangles

oh     ah     oa

ho     ha     ao

Trig Function Pattern

(Any Angle)

hint: circles

y/r     x/r     y/x

r/y     r/x     x/y

COT

(Acute Angles)

Adjacent

Opposite

COT

(Any Angle)

 x 

y

COT

(Real Numbers)

 x 

y

COTx

(Identity)

 1       or    cosx
tanx      sinx  

CSCx

(Identity)

  1   
sinx

CSC

(Acute Angles)

 Hypotenuse 

Opposite

CSC

(Any Angle)

 r 

y

CSC

(Real Numbers)

 1 

y

SEC

(Identity)

   1   

cosx

SEC

(Acute Angles)

 Hypotenuse 

Adjacent

SEC

(Any Angle)

 r 

x

SEC

(Real Numbers)

 1 

x

log_ax=y

x=a^y

Slope-Intercept Form

Answer: m=slope, b=y-intercept

y=mx+b

m=?  b=?

Quadratic Equation

-b±√(b²-4ac)

2a

Slope of a Line

m=y₂-y₁

     x₂-x₁

Midpoint Formula

(x₁+x_2, y₁+y₂₎

2          2

Midpoint of a Circle

(h,k)

Equation of a Circle

(x-h)²+(y-k)²=r²

Distance Formula

d=√(x₂-x₁)²+(y₂-y₁)²