Trig Review

Chapter 7
-Convert degrees to radians: degrees = pi over 180
-Convert radians to degrees: rads x 180 over pi = degrees
-k= 1/2r^2(theta)
-k= 1/2rs
-s= r(theta)
-Unit Circle= extremely important!

Chapter 8
-m= tan(alpha)
-csc(theta)=1/sin(theta)
-sec(theta)=1/cos(theta)
-cot(theta)=1/tan(theta)
-sin^2(theta) + cos^2(theta) = 1
-1 + tan^2(theta) = sec^2(theta)
-1 + cot^2(theta) = csc^2(theta)

Chapter 9
-SOHCAHTOA
-sin(theta)= opp/hyp
-cos(theta)= adj/hyp
-tan(theta)= opp/adj
-sin A/a = sinB/b = sinC/c
-Right triangle: 1/2bh
-Non right triangle: 1/2(adj leg)(adj leg)sin(angle below)
-Law of Cosines: leg^2= adj leg^2 + other adj leg^2 - 2(adj leg)(other leg)cos(angle below)

Chapter 10
-cos(alpha plus or minus beta) = cos(alpha)cos(beta) minus or plus sin(alpha)sin(beta)
-sin(alpah plus or minus beta)= sin(alpha)cos(beta) plus or minus cos(alpha)sin(beta)
-tan(alpha+beta) = tan(alpha + beta)/1-tan(alpha)tan(beta)
-tan(alpha-beta) = tan(alpha-beta)/1+tan(alpha)tan(beta)
-sin2(alpha)= 2sin(alpha)cos(alpha)
-cos2(alpha)= cos^2(alpha)-sin^2(alpha)
-cos2(alpha)= 1-2sin^2(alpha)
-cos2(alpha)= 2cos^2(alpha)-1
-tan2(alpha)= 2tan(alpha)/1-tan^2(alpha)
-sin(alpha)/2= plus or minus square root of 1-cos(alpha)/2
-cos(alpha)/2= plus or minus square root of 1+cos(alpha)/2
-tan(alpha)/2= plus or minus square root of 1-cos(alpha)/1+cos(alpha)
-tan(alpha)/2= sin(alpha)/1+cos(alpha)
-tan(alpha)/2= 1-cos(alpha)/sin(alpha)

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Ex.2:

A sector of a circle has arc length 10 cm and central angle 2.5 radians. Find its radius and area.
s = 11
Θ = 2.2
r = ??
You would use the formula to find the radius s = rΘ.
Plug into the formula and you get that r = 10/2.5= 4.
To find the area, you could use either K = ½r²Θ or K = ½rs .
K = ½(4²)2.5 = 20

r = 4 and K = 20