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PCHA midterm with complete verified solutions 2024.
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PCHA midterm with complete verified solutions 2024.
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PCHA midterm withcomplete verified
solutions 2024
sin (u +/- v) - answer sin(u)cos(v) +/- cos(u)sin(v)
cos (u +/- v) - answer cos(u)cos(v) +/- sin(u)sin(v)
sin(2u) - answer 2sin(u)cos(u)
sin(3x) - answer 3 sin(x) - 4 sin^3(x)
cos(2u) - answer cos^2(u)-sin^2(u)
1 - 2sin^2(u)
2cos^2(u) - 1
cos(3x) - answer 4cos^3(x) - 3cos(x)
tan(u +/- v) - answer tan(u) +/- tan(v) // 1 -/+ tan(u)tan(v)
tan(2u) - answer 2tan(u) // 1 - tan^2(u)
half-angle -- sin(u) - answer find sin(u) from 1 - 2sin^2(u)
half-angle -- cos(u) - answer find cos(u) from 2cos^2(u) - 1
, f(x + y) - answer f(x) + f(y)
even identities - answer f(-x) = f(x)
y = cos(x)
odd identities - answer f(-x) = -f(x)
y = sin(x)
y = tan(x)
pythagorean identities - answer sin^2(x)+cos^2(x)=1
1+tan^2(x)=sec^2(x)
1+cot^2(x)=csc^2(x)
co-function identities - answer csc(π/2 - x) = sec(x)
cos(π/2 - x) = sin(x)
cot(π/2 - x) = tan(x)
law of sines - answer sinA/a=sinB/b=sinC/c
law of cosines - answer c²=a²+b²-2abcosC
inverse restrictions - answer sin(x) = [-π/2, π/2]
csc(x) = [-π/2, π/2]
tan(x) = [-π/2, π/2]
cot(x) = [0, π]
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