Test 1 Flashcards
When is an angle quadrantal
If the terminal side is on an axis
Where is the Minute/Second notation for degrees on the calculator
Under apps, in the angles section (‘ or ‘’)
How do you turn 45°10’15’’ into degrees
Multiply the 10’ by 1/60 (bc min) and the 15’’ by 1/3600 (bc seconds) and add to 45° to get ~45.1708
How to turn 21.256 to DMS form
Multiply the .256 by 60 & round to get 15. Take the decimal that was on the 15 and multiply that by 60; round to get 22 to get: 22°15’22’’
what does one radian look like?
It’s the angle on a unit circle where the arc length & radius both equal 1
How should you format your test answers??
NO DECIMALS UNLESS SPECIFIED (even leave sqrts)
Circle sector area formula
A = πr²/2 * (x°/360°)
linear speed of circular moving object w/ variable explanation
v = s/t: v = linear speed, s = distance, t = time
Angular speed of circular moving object w/ variable explanation
ω = θ/t: ω = angular speed, θ = angle the object makes going around the circle; t = time
How are v & ω related? (hint: 4 steps to reach it) w/ variable explanation, & 2 resulting formulas
v = s/t = rθ/t = rω: linear speed = distance/time = (radius * central angle)/time = radius * angular speed
So: linear = radius * angular, and angular = linear/radius
how to find cscθ
Cosecant: hyp/opp or 1/sinθ
how to find secθ
Secant: hyp/adj or 1/cosθ
2 ways to handle sqrts on test
Don’t expand them; rationalize them
2 Comp. Angle Theorem (CAT) formulas and which angles they come from on the triangle
sinβ = cos α
tanβ = cot α
both of the angles other than the 90° one, which add up to 90°
Measures for 45-45-90 triangle
1-1-√2
Measures for 30-60-90 triangle
1-√3-2
what do π/3, π/4, & π/6 equal?
30°, 45°, 60°
Arc Length Formula
a = rθ: a = arc length, r = radius, θ = central angle
2 Quotient Identities
tanθ = sinθ/cosθ and cotθ = cosθ/sinθ
Pythagorean Identity
(sinθ)² + (cosθ)² = 1
angle of elevation
angle w/ rays straight out from eye and diagonal up to object
angle of depression
angle w/ ray straight out from one eye and diagonal down to object
what does “point on graph of” mean on the HW?
(angle put through the function, what it equals after) or (x, cos(x))
domain & range for sin
ARN; -1 to 1
D & R for cos
ARN; -1 to 1
D & R for tan
ARN except odd multiples of π/2; ARN
D & R for csc
ARN except any multiple of π; all but from -1 to 1
D & R for sec
ARN except odd multiples of π/2; all but from -1 to 1
D & R for cot
ARN except any multiple of π; ARN
periods for sin & cos
2π
period for tan
π
