ME3150 Trigonometric Identities

ME3150 Trigonometric Identities - Trigonometric Identities...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Trigonometric Identities a r b r a b sin( ) = cos ( ) = tan( ) = a (= r sin) r b (= r cos) cos 2 ( ) + sin 2 ( ) = 1 cos( ) = 1 - sin 2 ( ) sin( ) = 1 - cos 2 ( ) sin( ) cos() sin() cos( ) = sin( ) sin( + ) cos() - cos( + ) sin() = sin( ) cos( ) cos() sin( ) sin() = cos( m ) cos( + ) cos() + sin( + ) sin() = cos( ) sin(2 ) = 2 sin( ) cos( ) cos(2 ) = cos 2 ( ) - sin 2 ( ) = 2 cos 2 ( ) - 1 = 1 - 2 sin 2 ( ) - / 2 sin -1 ( ) / 2 tan( ) = 0 cos -1 ( ) - tan2 -1 ( ) sin( ) ; - / 2 tan -1 ( ) / 2 cos( ) sin 1st Quadrant: 0 1 / 2 sin(1 ) & tan(1 ) 0 , cos(1 ) 0 2nd Quadrant: / 2 2 cos( 2 ) & tan( 2 ) 0 , sin( 2 ) 0 3rd Quadrant: - 3 - / 2 sin(3 ) & cos( 3 ) 0 , tan(3 ) 0 4th Quadrant: - / 2 4 0 sin( 4 ) & tan( 4 ) 0 , cos( 4 ) 0 tan 2 1 4 cos 3 sin( - ) = - sin( ) cos( - ) = sin( ) 2 sin( + ) = cos( ) 2 cos( - ) = cos( ) sin( - ) = cos( ) 2 2 ) =1 sin( 2 cos( ) = 0 2 cos( + ) = - sin( ) sin( - ) = -1 2 cos( - ) = 0 2 sin(0) = 0 cos(0) = 1 sin( ) = 0 cos( ) = -1 For small << 1 rad: Combining sines & cosines: sin( ) 2 cos( ) 1 - 1 2 if x (t ) = A cos( - ) = A1 cos( ) + A2 sin() or x = A cos( + ) = A1 cos( ) - A2 sin() then A = A12 + A2 2 A & = tan -1 ( 2 ) A1 if x = A sin( + ) = A1 cos( ) + A2 sin() or x = A sin( - ) = A1 cos( ) - A2 sin() then A = A12 + A2 2 A & = tan -1 ( 1 ) A2 Integration by part: u dv = uv - v du t cos(t ) dt = cos(t ) + t sin(t ) 1 1 t sin(t ) dt = sin(t ) - t cos(t ) 1 1 ...
View Full Document

Page1 / 2

ME3150 Trigonometric Identities - Trigonometric Identities...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online