Chapter 6 Law Of Sines And Cosines Flashcards
When do you use the law of sines
When you know 2 angles and any side AAS
Or
2 sides and an angle opposite one of them. ASA
What is the law of sines
a. =. b. =. c
——- —— ——
sinA. sinB. sinC
What is the law of cosines
a^2 = b^2 + c^2 - 2bc(cosA)
Alternative form:
cosA = b^2 + c^2 - a^2
——————-
2bc
When do you use the law of cosines
Three sides of a triangle SSS
two sides and an includes angle of a triangle SAS
What is the formula for the area of an oblique triangle
1
A= – bc sinA
2
What is Heron’s formula
A = square root of s(s-a)(s-b)(s-c)
What does s stand for in Heron’s formula and what is the formula to find s
Semi perimeter
a + b + c s = -----------
2
What is the trigonometric for of a complex number
Z = a + bi Z = r. (Cos theta + isin theta) 1. 1 r = square root of a^2 + b^2 tan theta = b / a a = r cos theta b = r sin theta
How do you find the trigonometric form of a complex number
Discover quadrant
Find r
Find theta
Pug it in into equation:
Z. = r. (cos theta + isin theta)
1. 1
Formula to multiply complex numbers trigonometric form
Z1 Z2 = r1 r2 (cos(theta1 + theta2) +
isin (theta1 + theta2)
What is the trigonometric form and the standard form of complex numbers
Trigonometric: equation containing z and r
Standard: a + bi
Formula to divide complex numbers
Z1. r1
— = — [ cos(theta1 - theta2) + isin
Z2. r2. (theta1 - theta2)]
What is demoivres theorem
Z^n = [r (cos theta + isin theta) ] ^n
Other known as:
Z^n = r^n (cos n theta + isin n theta)
What are the steps for demoivre’s theorem
Convert to trig form Find r value Find theta value Quadrant # plug in Demoivres theorem
Nth root of complex numbers
Z = u^n = ( a + bi ) ^n
\_\_\_\_ Theta + 2kpie
n _/ r (cos -------------- +
n
Theta + 2kpie
isin --------------- )
n
