Pre Calculus Chapter 4 Exam Questions with Verified Solutions (Graded A+)
To find co-terminal angels... - Answers ±360º or ± 2π
In one full revolutions there are how many radians? - Answers 6.28 radians (or 2π radians)
To convert from degrees to radians multiply by... - Answers π / 180º
To convert from radians to degrees - Answers 180º / π
Arc Length= ? in degrees - Answers (θº/360º) ∙ 2πr, (where theta is in degrees and r is radius)
Arc Length = ? in radians - Answers Arclength= rθ, (where theta is in radians and r is radius)
Unit Circle Picture - Answers (Add pic)
The reference angle is the acute angle formed from the terminal side to the x axis. Always positive! -
Answers (Add Pic of a terminal angle, hand draw it)
Quadrant 1 - Answers All are trig ratios positive
Quadrant 2: - Answers Only sine is positive
Quadrant 3 - Answers Only tan is positive (because both Sin and Cos are negative)
Quadrant 4 - Answers Only cosine is positive.
Picture of quadrants - Answers (add a pic drawn by hand)
Sec= - Answers 1/cosθ (hyp/adj)
Csc= - Answers 1/sinθ (hyp/opp)
Cot= - Answers 1/tanθ (adj/opp)
tanθ= - Answers (sinθ/cosθ)
cotθ= - Answers (cosθ/sinθ)
pythagorean identity - Answers sin²θ + cos²θ = 1
Amplitude= - Answers | a | {in y= a sin (bx + c) + d}
General equation for sin graphs - Answers y= a sin (bx + c) + d
Period = - Answers 2π / b
Gap= - Answers period / 4
Vertical shift= - Answers d
To find co-terminal angels... - Answers ±360º or ± 2π
In one full revolutions there are how many radians? - Answers 6.28 radians (or 2π radians)
To convert from degrees to radians multiply by... - Answers π / 180º
To convert from radians to degrees - Answers 180º / π
Arc Length= ? in degrees - Answers (θº/360º) ∙ 2πr, (where theta is in degrees and r is radius)
Arc Length = ? in radians - Answers Arclength= rθ, (where theta is in radians and r is radius)
Unit Circle Picture - Answers (Add pic)
The reference angle is the acute angle formed from the terminal side to the x axis. Always positive! -
Answers (Add Pic of a terminal angle, hand draw it)
Quadrant 1 - Answers All are trig ratios positive
Quadrant 2: - Answers Only sine is positive
Quadrant 3 - Answers Only tan is positive (because both Sin and Cos are negative)
Quadrant 4 - Answers Only cosine is positive.
Picture of quadrants - Answers (add a pic drawn by hand)
Sec= - Answers 1/cosθ (hyp/adj)
Csc= - Answers 1/sinθ (hyp/opp)
Cot= - Answers 1/tanθ (adj/opp)
tanθ= - Answers (sinθ/cosθ)
cotθ= - Answers (cosθ/sinθ)
pythagorean identity - Answers sin²θ + cos²θ = 1
Amplitude= - Answers | a | {in y= a sin (bx + c) + d}
General equation for sin graphs - Answers y= a sin (bx + c) + d
Period = - Answers 2π / b
Gap= - Answers period / 4
Vertical shift= - Answers d
