Sum and Difference Identities:(sin)
sin (a + b) = sin(a)cos(b) + cos(a)sin(b)
sin (a - b) = sin(a)cos(b) - cos(a)sin(b)
Sum and Difference Identities:(cos )
cos (a + b) = sin(a)sin(b) - cos(a)cos(b)
cos (a - b) = sin(a)sin(b) + cos(a)cos(b)
Which Function goes with the graph? sin
crosses the Y axisat midpoint
cos crosses the Y axis
at high (or low) point
sec and tan cross the y axis
csc and cot have asymptotes at Y
axis
How to find Coterminal Angles:
Coterminal = Given ± Coterminal = Given ± kk(2π)(2π) + if angle is negative - if angle is positive
KK ≈ Given /2π≈ Given /2π (round upup if angle is negative, round downdown if angle is positive)
Remember: 2π = 360°
Hint on finding Coterminal Angles in radians:
Coterminal = Coterminal = ΘΘ ± ± kk(2π)(2π) + if angle is negative - if angle is positive
Convert Convert 2π 2π to match to match denominators with denominators with ΘΘ, then k , then k
is easy to solveis easy to solve 2π 2π == 4π/2 4π/2 == 6π/3 6π/3 == 8π/4 8π/4 == 12π/6 12π/6
How do you convert between radians and
degrees?
So by dimensional analysis:
X° (π/180 ° ) = Θ radiansAnd
Θ radians (180 °/π) = X°
A useful mnemonic for certain values of sines and cosines
For certain simple angles, the sines and cosines take the form for 0 ≤ n ≤ 4, which makes them easy to remember.
Trig Co-function Identities:
* Co-Function for Sine:
* Co-Function for Cosine:
* Co-Functions for Tangent:
* Co-Function for Cotangent:
* Co-Function for Secant:
* Co-Function for Cosecant:
sin a = cos (π/2 – a)
cos a = sin (π/2 – a)
tan a = cot (π/2 – a)
cot a = tan (π/2 – a)
sec a = csc (π/2 – a)
csc a = sec (π/2 – a)