860 CHAPTER 8 Applications of Trigonometry Chapter 8 Test Prep Key Terms 8.1 Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Side-Side-Side (SSS) Side-Angle-Angle (SAA) oblique triangle ambiguous case 8.2 semiperimeter 8.3 scalar vector quantity vector magnitude initial point terminal point parallelogram rule resultant opposite (of a vector) zero vector newton equilibrant airspeed ground speed 8.4 position vector horizontal component vertical component direction angle unit vector dot product (inner product) angle between two vectors orthogonal vectors 8.5 real axis imaginary axis complex plane rectangular form (of a complex number) trigonometric (polar) form (of a complex number) absolute value (modulus) argument 8.6 nth root (of a complex number) 8.7 polar coordinate system pole polar axis polar coordinates rectangular (Cartesian) equation polar equation cardioid polar grid rose curve lemniscate spiral of Archimedes limaçon 8.8 plane curve parametric equations (of a plane curve) parameter ellipse trochoid cycloid Quick Review Concepts Examples In triangle ABC, find c, to the nearest hundredth, if A = 44°, C = 62°, and a = 12.00 units. a sin A = c sin C Law of sines 12.00 sin 44° = c sin 62° Substitute. c = 12.00 sin 62° sin 44° c ≈15.25 units Use a calculator. For triangle ABC above, apply the appropriate formula to find the area. Here, B = 180° - 44° - 62° = 74°. = 1 2 ac sin B= 1 2 112.002115.252 sin 74°≈87.96 sq units 8.1 The Law of Sines Law of Sines In any triangle ABC, with sides a, b, and c, the following hold true. a sin A = b sin B = c sin C sin A a = sin B b = sin C c Alternative form Area of a Triangle In any triangle ABC, the area is half the product of the lengths of two sides and the sine of the angle between them. = 1 2 bc sin A, = 1 2 ab sin C, = 1 2 ac sin B Multiply by sin 62° and rewrite. New Symbols OP or OP> vector OP ∣ OP∣ magnitude of vector OP 8 a, b 9 position vector i, j unit vectors cis U cos u + i sin u
RkJQdWJsaXNoZXIy NjM5ODQ=