

Datrysiad Cyffredinol mewn Radiannau
Presentation
•
Mathematics
•
11th Grade
•
Practice Problem
•
Easy
Llio Davies
Used 5+ times
FREE Resource
5 Slides • 7 Questions
1
Datrysiad Cyffredinol mewn Radiannau
General Solution in Radians
Mathemateg Bellach Uned 4
Further Maths Unit 4
2
Sin x
PV + 2πn
SV + 2πn
Mae sin yn ailadrodd bob 360o felly bob 2π radian.
Sine repeats every 360o so every 2π radians.
3
Cos x
± PV + 2πn
Mae cos hefyd yn ailadrodd bob 360o felly bob 2π radian.
Cosine also repeats every 360o so every 2π radians.
4
Tan x
PV + πn
Mae tan yn ailadrodd bob 180o felly bob π radian.
Tan repeats every 180o so every π radians.
5
Multiple Choice
Datrysiad cyffredinol sin x = 1/2 yw ...
The general solution of sin x = 1/2 is ...
x = ± π/6 + 2πn
x = π/6 + 2πn,
x = 5π/6 + 2πn
x = π/6 + πn
x = π/6 + 2πn,
x = 11π/6 + 2πn
6
Match
Parwch y canlynol.
Match the following.
sin x = √3/2
cos x = 1/2
tan x = √3
sin x = 0
cos x = 0
x = π/3 + 2πn,
x = 2π/3 + 2πn
x = ± π/3 + 2πn
x = π/3 + πn
x = πn
x = ± π/2 + 2πn
x = π/3 + 2πn,
x = 2π/3 + 2πn
x = ± π/3 + 2πn
x = π/3 + πn
x = πn
x = ± π/2 + 2πn
7
Onglau Cyfansawdd
Compound Angles
sin (2x) = 1/2
2x = π/6 + 2πn, 2x = 5π/6 + 2πn
x = π/12 + πn, x = 5π/12 + πn
Darganfod y datrysiad cyffredinol ar gyfer 2x.
Find the general solution for 2x.
YNA rhannu trwodd hefo 2.
THEN divide by 2.
8
Multiple Choice
tan (x/2) = √3
x/2 = π/3 + πn
x = (π/6) + πn/2
x = (2π/3) + πn/2
9
Drag and Drop
2x =
x =
10
Hotspot
Chwiliwch y gwall.
Spot the error.
11
Multiple Choice
cos (4x) = √2/2
x = ± π/4 + 2πn
x = π/16 + πn/2
x = 15π/16 + πn/2
x = ± π/16 + πn/2
x = π/4 + 2πn
x = 3π/4 + 2πn
12
Drag and Drop
cos 4x + 2 cos (6x+2x)/2 cos (6x-2x)/2 = 0
cos 4x + 2 cos
cos 4x (1 + cos 2x) = 0
cos 4x = 0 and cos 2x = -1
Datrysiad Cyffredinol mewn Radiannau
General Solution in Radians
Mathemateg Bellach Uned 4
Further Maths Unit 4
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