MAT170 SPR 2009 Material for 3rd Quiz

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) 

Pythagorean Identities

Reciprocal Identities

Quotient Identities

Even-Odd Identites

Functions sin & cos

Functions tan & cot

Functions sec & csc:

Which Function goes with the graph?  sin crosses the Y axis at 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 ± k(2π)  Coterminal = Given ± k(2π) + if angle is negative - if angle is positive  K ≈ Given /2π up down  K ≈ Given /2π (round up if angle is negative, round down if angle is positive)  Remember: 2π = 360°

Hint on finding Coterminal Angles in radians:  Coterminal = Θ ± k(2π)  Coterminal = Θ ± k(2π) + if angle is negative - if angle is positive  Convert 2π to match denominators with Θ, then k is easy to solve  2π = 4π/2 = 6π/3 = 8π/4 = 12π/6

How do you convert between radians and degrees? So by dimensional analysis: X° ( π / 180 ° ) = Θ radians And Θ radians ( 180 ° / π ) = X°

Formula for length of an arc: Θ must be in radians

Linear speed of a point on a circle: Distance/time Where S = RΘ

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.

30º =

45º =

60º =

sin П 6.

cos П 6.

tan П 6.

When you remember what is underneath, Click the shape to make certain.

. A B C Θ

tan Θ = X = cos Θ Y = sin Θ tan Θ =

cot Θ = X = cos Θ Y = sin Θ cot Θ =

sec Θ = X = cos Θ Y = sin Θ sec Θ =

csc Θ = X = cos Θ Y = sin Θ csc Θ =

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)