CHAP. 6 TRIG

What is the circular function for sin θ?

y/r = y

What is the circular function for cos θ?

x/r = x

What is the circular function for tan θ?

y/x . x does not equal 0

What is the reciprocals for csc, sec, and cot θ?

csc θ= sin θ

sec θ= cos θ

cot θ= tan θ

What is the circular function for csc θ?

r/y = 1/y (y does not equal 0)

What is the circular function of sec θ?

r/x = 1/x (x does not equal 0)

What is the circular function of cot θ?

x/y (y does not equal 0)

What’s the common angle and (x,y) for pi/2

angle: 90 degrees

(0,1)

What’s the common angle and (x,y) for pi/4

angle: 45 degrees

(square root of 2 over 2, square root of 2 over 2)

What’s the common angle and (x,y) for pi/6

angle: 30 degrees

(square root of 3 over 2, 1/2)

What’s the common angle and (x,y) for pi/3

angle: 60 degrees
(1/2, square root of 3 over 2)

What is positive and negative in quad 1?

All is positive

What is positive and negative in quad 2?

sin, csc is positive

everything else is negative

What is positive and negative in quad 3?

tan, cot is positive

others are negative

What is positive and negative in quad 4?

cos, sec is positive

others are negative

What are even properties?

cos(-θ) = cos θ

sec(-θ) = sec θ

What are odd properties?

sin(-θ) = -sin θ

csc(-θ) = -csc θ

tan(-θ) = -tan θ

cot(-θ) = -cot θ

How do you convert to radian from degrees?

degrees times (pi over 180 degrees)

How do you convert to degrees from radians?

radians times (180 degrees over pi)

What’s the equation for arc length?

s = rθ

What’s the equation for area of a sector?

A = (1/2)r²θ

What’s the equation for Angular speed?

w = θ/t

What’s the equation for Linear speed

v = s/t

s = radius times central angle

but it can also be be rewritten in terms of angular speed: v=radius times angular speed

What is sine’s graph? What’s it’s pattern? and reflected?

Period is 2pi, odd function
MUMD

MDMU

What is cosine’s graph pattern? and reflected?

Period is 2pi, even function

UMDM

DMUM

What graph is this? What’s it’s pattern? And reflected?

Tangent

Pattern: MUAD

Reflected: MDAU

What graph is this? What’s it’s pattern? And reflected?

Cotangent

Pattern: AUMD

Reflected: ADMU

What is the right triangle equation for cosine?

adjacent/hypotenuse

What is the right triangle equation for sine?

opposite/hypotenuse

What is the right triangle equation for tangent?

opposite/adjacent

What is the pythagorean theorem for these right triangles?

opposite² + adjacent² = hypotenuse²