ALEKS PPL Exam with Accurate
Solutions
circle equation - ANSWER-(x-h)^2 + (y-k)^2 = r^2
sine - ANSWER-opposite/hypotenuse
cos - ANSWER-adjacent/hypotenuse
tan - ANSWER-opposite/adjacent
Sec - ANSWER-1/cos or hypotenuse/adjacent
Cosecant - ANSWER-1/sine or hypotenuse/opposite
Cotangent - ANSWER-1/tan or adjacent/opposite
Inverse Trig Functions - ANSWER-Example: if given sin^-1= 1/2, can be formulated as
sin (?) = 1/2
Sum and Difference Formulas - ANSWER-sin (x + y) = sin x cos y + cos x sin y
sin (x- y) = sin x cos y - cos x sin y
cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y
tan (x + y ) = (tan x + tan y)/(1 - tan x tan y)
tan (x - y) = (tan x - tan y)/(1 + tan x tan y)
coterminal angles - ANSWER-add 360 if negative or subtract 360 if positive
Reference angle - ANSWER-Quad 1: reference angle
Quad 2: 180-angle
Quad 3: angle - 180
Quad 4: 360- quad 4
To find a negative degree, find coterminal then find the reference angle.
How to remember unit circle - ANSWER--pattern starts with rad 3, rad 2, 1. Rad 3
always goes with 1/2 and rad 2 always goes with rad 2.
-6, 4, 3 as denominators. Quad 2 is -1, Quad 3 is +1, Quad 4 is adding denom and num
of Quad 2.
Solutions
circle equation - ANSWER-(x-h)^2 + (y-k)^2 = r^2
sine - ANSWER-opposite/hypotenuse
cos - ANSWER-adjacent/hypotenuse
tan - ANSWER-opposite/adjacent
Sec - ANSWER-1/cos or hypotenuse/adjacent
Cosecant - ANSWER-1/sine or hypotenuse/opposite
Cotangent - ANSWER-1/tan or adjacent/opposite
Inverse Trig Functions - ANSWER-Example: if given sin^-1= 1/2, can be formulated as
sin (?) = 1/2
Sum and Difference Formulas - ANSWER-sin (x + y) = sin x cos y + cos x sin y
sin (x- y) = sin x cos y - cos x sin y
cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y
tan (x + y ) = (tan x + tan y)/(1 - tan x tan y)
tan (x - y) = (tan x - tan y)/(1 + tan x tan y)
coterminal angles - ANSWER-add 360 if negative or subtract 360 if positive
Reference angle - ANSWER-Quad 1: reference angle
Quad 2: 180-angle
Quad 3: angle - 180
Quad 4: 360- quad 4
To find a negative degree, find coterminal then find the reference angle.
How to remember unit circle - ANSWER--pattern starts with rad 3, rad 2, 1. Rad 3
always goes with 1/2 and rad 2 always goes with rad 2.
-6, 4, 3 as denominators. Quad 2 is -1, Quad 3 is +1, Quad 4 is adding denom and num
of Quad 2.
