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Special Factoring ( )( ( ) ( ) ( )( ( )( Arc Length and Angular Speed ) Dimensional analysis conversion factors ) ) Converting Between Degree & Radian Measure To convert from degree to radian measure, multiply by To convert from radian to degree measure, multiply by Variables ( ( ) ) ( ( Trig Functions of an Acute Angle Trigonometric Identities Reciprocal Identities , Cofunction Identities ( ) , ( ) , ( ) , ( ) , ( ) , ( ) Ratio Identities , Odd-Even Identities ( ) , ( ) , Double-Angle Identities ( ( ) ) , , ( ( ) ) Pythagorean Identities Half-Angle Identities √ √ √ Sum and Difference Identities ( ) ( ) ( ) ( ) ( ) ( ) Solving Triangles Law of Sines Law of Cosines Area of a Triangle ) ) Vectors The component form of ⃗⃗⃗⃗⃗ with The magnitude of a vector ( ) and ( with component form 〈 ) is ⃗⃗⃗⃗⃗ 〉 is |⃗ | 〈 〉 √ 〉 is given by The reference angle for the direction angle of the vector 〈 . Figure out which quadrant this angle should be in and measure the angle counterclockwise from the positive x-axis. The horizontal component of the vector 〈 The vertical component of the vector 〈 Vector Addition/Subtraction: If ⃗ ⃗ , then is a vector and ⃗ |⃗ | | | | | 〉, the scalar product of 〈 〉 and 〈 〉, then ⃗ and is 〈 〉 〈 ⃗ 〈 〉. The vector is a 〉. is a unit vector (vector with magnitude 1) in the direction of . 〈 The dot product of two vectors ⃗ If 〉 is 〈 For a real number and a vector scalar multiple of the vector . If 〉 is 〉 and 〈 is the angle between two nonzero vectors ⃗ and , then 〉 is ⃗ ⃗ . ⃗⃗ ⃗ |⃗⃗ ||⃗ | . Trigonometric Form of Complex Numbers , where √ , where A complex number ( ) or [ ( [ ( [ ( ) ) ) ( ( ( )] )] )] ( ) can be written in trigonometric form as is the modulus of and direction angle √ is referred to as the argument.