Trigonometry Basics for Exam1
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Arc length
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S=rθ
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Area of a sector
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A=1/2r2θ
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Linear speed
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V=s/t=rθ/t=rw
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Angular speed
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w=θ/t
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R
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r=√x2 + y2
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Sin θ=y/r
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Csc θ=r/y
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Cos θ=x/r
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Sec θ=r/x
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Tan θ=y/x
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Cot θ=x/y
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Acute
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Less than 90
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Right
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90
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Obtuse
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More than 90, less than 180
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Straight
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180
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Sinθ=opp/hyp
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Cscθ=hyp/opp
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Cosθ=adj/hyp
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Secθ=hyp/adj
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Tanθ=adj/opp
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Cotθ=app/adj
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Reciprocal Identities
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sinθ=1/csc
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cscθ=1/sin
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cosθ=1/sec
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secθ=1/cos
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tanθ=1/cot
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cotθ=1/tan
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Pythagorean Identities
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sin2θ + cos2θ=1
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1+tan2θ=sec2θ
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1+cot2θ=csc2θ
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Quotient Identities
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tanθ=sinθ/cosθ
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cotθ=cosθ/sinθ
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Odd
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Even
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sin(-t)=-sin t
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cos(-t)=cos t
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csc(-t)=-csc t
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sec(-t)=sec t
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tan(-t)=-tan t
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cot(-t)=-cot t
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