Download Lone Star College-CyFair Formula Sheet

Lone Star College-CyFair Formula Sheet
The following formulas are critical for success in the indicated course. Student
CANNOT bring these formulas on a formula sheet or card to tests and instructors
MUST NOT provide them during the test either on the board or on a handout.
They MUST be memorized.
Math 1314 College Algebra
Math 1316 Trigonometry
Students in Trigonometry should know all the formulas from Math 1314 College
Algebra plus the following.
Library of Trigonometric Functions
Math 2412 Precalculus
Students in Precalculus should know all the formulas from Math 1314 College
Algebra and Math 1316 Trigonometry plus the following.
Half Angle Formulas
1− cos 2θ
sin θ = ±
2
cosθ = ±
1+ cos 2θ
2
tan θ =
1− cos 2θ
sin 2θ
Products and Quotients of Complex Numbers in Polar Form
Let z1 = r1 (cosθ1 + i sin θ1 ) and z2 = r2 (cosθ 2 + i sin θ 2 ) . Then
z1z2 = r1r2 [ cos(θ1 + θ 2 ) + i sin(θ1 + θ 2 )]
and, if z2 ≠ 0,
z1 r1
= [ cos(θ1 − θ 2 ) + i sin(θ1 − θ 2 )]
z2 r2
DeMoivre’s Theorem
If z = r(cosθ + i sin θ ) and n is a positive integer,
z n = r n [ cos(nθ ) + i sin(nθ )]
Complex Roots
Let w = r(cosθ 0 + i sin θ 0 ) be a complex number and let n ≥ 2 be an integer. If
w ≠ 0, there are n distinct complex nth roots of w, given by the formula
2kπ ⎞
2kπ ⎞ ⎤
⎡ ⎛θ
⎛θ
zk = n r ⎢ cos ⎜ 0 +
+ i sin ⎜ 0 +
⎟
⎟
⎝ n
n ⎠
n ⎠ ⎥⎦
⎣ ⎝ n
where k = 0,1,2,…,n − 1