Download Calculus Handout Unit Circle: Right Angle Trigonometry Fundamental Identities

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Transcript 
Calculus Handout
Trig Summary
Unit Circle:
Right Angle Trigonometry:
opp
adj
sin θ =
cos θ =
hyp
hyp
csc θ =
hyp
opp
sec θ =
hyp
adj
Fundamental Identities:
1
sin θ
csc θ =
tan θ =
sin θ
cos θ
sin2 θ + cos2 θ = 1
Half Angle Formulas:
1 − cos(2x)
sin2 x =
2
1
cos θ
1 + tan2 θ = sec2 θ
Addition and Subtraction Formulas:
sin(x ± y) = sin x cos y ± cos x sin y
Double Angle Formulas:
sin 2x = 2 sin x cos x
sec θ =
tan θ =
opp
adj
cot θ =
adj
opp
cot θ =
cos θ
1
=
sin θ
tan θ
1 + cot2 θ = csc2 θ
cos(x ± y) = cos x cos y ∓ sin x sin y
cos 2x = cos2 x − sin2 x = 2 cos2 x − 1 = 1 − 2 sin2 x
cos2 x =
1 + cos(2x)
2
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