Stephanie's Reflection

Trig Chart:
0°
sin0=0
cos0=1
tan0=0
csc0=undefined
sec0=1
cot0=0
30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3
45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1
60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2
90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0

Reference Angles (must be between 0° and 90°)
1)find which quadrant angle is in
2)determine the sign in that quadrant (+ve or -ve)
3)subtract 180° until the angle is between 0° and 90° (0 and π/2)

1)find the reference angle using chart or calculator
2)find what quadrant you need to be in based on the sign of the value
3)use notes to move to that quadrant
To Move:
I to IV = make negative and add 360°
I to III = add 180°
I to II = make negative and add 180°
II to IV = add 180°

Unit Circle

sin theta = y/r

cos theta = x/r

tan theta = y/x

csc theta = r/x

sec theta = x/y

cot theta = x/y

r=sqrtx^2+y^2

90 pi/2
180 pi
270 3pi/2
360 2pi

sin pos in one and two and neg in three and four

cos pos in one and four and neg in two and three

tan pos in one and three and neg in two and four

cot pos in one and neg in two three and four

sec pos in one and neg in two three and four

csc pos in one and two and neg in three and four

AREA OF A NON-RIGHT TRIANGLE
A=1/2(leg)(leg)sin(angle between)

RIGHT TRIANGLES

• hypotenuse opposite angle
• a=1/2bh
• SOHCAHTOA

sin theta=opposite/hypotenuse
cos theta=adjacent/hypotenuse
tan theta=opposite/adjacent

LAW OF SINES
sinA/a sinB/b sinC/c

• used when you know pairs in a non-right triangle
• you are setting up proportions

Right Triangles

• A=1/2bh
• SOHCAHTOA
• sinΘ=opposite leg/hypotenuse
• cosΘ=adjacent leg/hypotenuse
• tanΘ=opposite leg/adjacent leg

Law of Cosines
(opposite leg)²=(adjacent leg)² + (other leg)² - 2(adjacent leg)(adjacent leg)cos°
EG: x, 5, 6 angle = 35°
x²=5²+6²-2(5)(6)cos35°
x=√(5²+6²-2(5)(6)cos35°)
x≈3.443

Area of Inscribed Shapes
A=nr²sinΘcosΘ

SOLVING TRIG EQUATIONS

for any line m = tan alpha
m = slope , alpha = angle of inclination
For a conic: tan 2 alpha = B/A-C
if A=C then pi/4
A = coefficient of x^2, B = coefficient of xy, C = coefficient of y^2

y=Asin(Bx-h)+C
amplitude is hight
b is period p=2π/b
h is horizontal shift
c is vertical shift

Identities:

1. check identities
2. algebra
3. identities

Reciprocal Relationships

• cscΘ=1/sinΘ
• secΘ=1/cosΘ
• cotΘ=1/tanΘ

Relationships with Negatives

• sin -Θ= -sinΘ and cos -Θ= -cosΘ
• csc -Θ= -cscΘ and sec -Θ= -secΘ
• tan -Θ= -tanΘ and cot -Θ= -cotΘ

Pythagorean Relationsihps

• sin²Θ+cos²Θ=1
• 1+tan²Θ=sec²Θ
• 1+cot²Θ=csc²Θ

Cofunction Relationships

• sinΘ=cos(90°-Θ) and cosΘ=sin(90°-Θ)
• tanΘ=cot(90°-Θ) and cotΘ=tan(90°-Θ)
• secΘ=csc(90°-Θ) and cscΘ=sec(90°-Θ)