CHAPTER 8 KEY FORMULAS AND EQUATIONS

A graph represents diagonal straight line to form right angle triangle with angle, theta and 90. The adjacent is y, hypotenuse as r, and opposite as x. The coordinate is (x, y).

Fig. 1
sin θ = yrcsc θ = rycos θ = xrsec θ = rxtan θ = yxcot θ = xy(8.1)
trig θ =  ±  trig θref ("trig" is any trigonometric function)(8.2)
A unit circle centered at (0, 0) passes through (1, 0), (x, y), (0, 1), (negative 1, 0), and (0, negative 1). Central angle theta has a terminal side with length r = 1 that rises through (x, y).

Fig. 1
θ = θref(quadrant I)θ = 180 °  + θref(quadrant III)θ = 180 °  − θref(quadrant II)θ = 360 °  − θref(quadrant IV)(8.3)
sin θ = ycsc θ = 1ycos θ = xsec θ = 1xtan θ = yxcot θ = xy(8.4)

Negative angles
sin( − θ) =  − sin θcos( − θ) = cos θtan( − θ) =  − tan θcsc( − θ) =  − csc θsec( − θ) = sec θcot( − θ) =  − cot θ
(8.5)

Radian-degree conversions
π rad = 180 ° (8.6)
1 °  = π180rad = 0.01745 rad(8.7)
1 rad = 180 ° π = 57.30 ° (8.8)

Circular arc length
s = θr(θ in radians)(8.9)

Circular sector area
A = 12θr2(θ in radians)(8.10)

Linear and angular velocity
v = ωr(8.11)
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