6.1 Conversion of Angular Measure Degree/Radian Relationship: 180° = p radians Conversion Formulas: From To Multiply by Degrees Radians p 180 Radians Degrees 180° p 7.3 Cofunction Identities cos190° - u2 = sin u sin190° - u2 = cos u tan190° - u2 = cot u cot190° - u2 = tan u sec190° - u2 = csc u csc190° - u2 = sec u 7.4 Double-Angle and Half-Angle Identities cos 2A = cos2 A - sin2 A cos 2A = 1 - 2 sin2 A cos 2A = 2 cos2 A - 1 sin 2A = 2 sin A cos A tan 2A = 2 tan A 1 - tan2 A cos A 2 = {B1 + cos A 2 sin A 2 = {B1 - cos A 2 tan A 2 = {B1 - cos A 1 + cos A tan A 2 = sin A 1 + cos A tan A 2 = 1 - cos A sin A 7.1 Fundamental Identities cot u = 1 tan u sec u = 1 cos u csc u = 1 sin u tan u = sin u cos u cot u = cos u sin u sin2 u + cos2 u = 1 tan2 u + 1 = sec2 u 1 + cot2 u = csc2 u sin1-u2 = -sin u cos1-u2 = cos u tan1-u2 = -tan u csc1-u2 = -csc u sec1-u2 = sec u cot1-u2 = -cot u 7.3 Sum and Difference Identities cos1A + B2 = cos A cos B - sin A sin B cos1A - B2 = cos A cos B + sin A sin B sin1A + B2 = sin A cos B + cos A sin B sin1A - B2 = sin A cos B - cos A sin B tan1A + B2 = tan A + tan B 1 - tan A tan B tan1A - B2 = tan A - tan B 1 + tan A tan B 7.4 Product-to-Sum and Sum-to-Product Identities cos A cos B = 1 2 3cos1A + B2 + cos1A - B24 sin A sin B = 1 2 3cos1A - B2 - cos1A + B24 sin A cos B = 1 2 3sin1A + B2 + sin1A - B24 cos A sin B = 1 2 3sin1A + B2 - sin1A - B24 sin A + sin B = 2 sin a A + B 2 b cos a A - B 2 b sin A - sin B = 2 cos a A + B 2 b sin a A - B 2 b cos A + cos B = 2 cos a A + B 2 b cos a A - B 2 b cos A - cos B = -2 sin a A + B 2 b sin a A - B 2 b 6.1 Applications of Radian Measure Arc Length: s = ru, u in radians Area of Sector: = 1 2 r2 u, u in radians 6.2 Angular Speed V Linear Speed v v = u t v = s t (v in radians per unit time, u in radians) v = ru t v = rv 8.1 Law of Sines In any triangle ABC, with sides a, b, and c, a sin A = b sin B , a sin A = c sin C , and b sin B = c sin C . Area of a Triangle The area of a triangle is given by half the product of the lengths of two sides and the sine of the angle between the two sides. = 1 2 bc sin A, = 1 2 ab sin C, = 1 2 ac sin B 8.2 Law of Cosines In any triangle ABC, with sides a, b, and c, a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, and c2 = a2 + b2 - 2ab cos C. Heron’s Area Formula If a triangle has sides of lengths a, b, and c, with semiperimeter s = 1 21a + b + c2, then the area of the triangle is = 2s1s - a21s - b21s - c2. Identities and Formulas
RkJQdWJsaXNoZXIy NjM5ODQ=