Trigonometry (5) Flashcards
Endpoints for arcsine
(1,pi/2) and (-1,-pi/2)
(1,pi/2) and (-1,-pi/2)
Endpoints for arcsine
Endpoints for arccosine
(-1, pi) and (1,0). Crosses the y-axis at (0,pi/2)
(-1, pi) and (1,0). Crosses the y-axis at (0,pi/2)
Endpoints for arccosine
Asymptotes for arctangent
y = pi/2 and y=-pi/2
y = pi/2 and y=-pi/2
Asymptotes for arctangent
Working out cos x = -(1/2)
(cos^-1)(-1/2)
(cos^-1)(-1/2)
Working out cos x = -(1/2)
Interval of sin 3x for 0<=x<=2pi
0<=3x<=6pi
0<=3x<=6pi
Interval of sin 3x for 0<=x<=2pi
Range for 2cos(x - pi/4) = ¬3 for 0<=x<=2pi
-pi/4 <= x - pi/4 <= 2pi - pi/4
Approximate cos(pi/12)
1 - (1/2)(pi/12)^2 = 0.966
1 - (1/2)(pi/12)^2 = 0.966
Approximate cos(pi/12)
Find the small angle approximation for cosec^2pheta
1/pheta^2
1/pheta^2
Find the small angle approximation for cosec^2pheta
Find the small angle approximation for sin^2pheta * cospheta
pheta^2 * (1-(1/2)pheta^2) = pheta^2 -(1/2)pheta^4
Write 9sinx+12cosx in the form R sin (x+a)
9sinxcosa + 12cosxsina R cos a = 9, R sin a = 12 tan^-1(12/9) = 0.9272... ¬(12^2 + 9^2) = 15 9sinx+12cosx = 15 sin (x + 0.927)
Solve 9sinx + 12cosx = 3 for ranges 0<=x<=2pi
As 9sinx+12cosx = 15 sin (x + 0.9272...) 15 sin (x + 0.9272...) = 3 => sin (x + 0.9272...) = 0.2 0.9272...<= x + 0.9272... <= 7.2104...
draw sinx
x + 0.9272… = sin^-1(0.2)
x + 0.9272… = 0.2013…
(This is outside the range)
pi - 0.2013… = 2.940…
2pi + 0.2013… = 6.484…
(x + 0.9272…) = 2.940… and 6.484
x = 2.01 and 5.56
Find the maximum and minimum value of f(x) = 10 - 9 sin x - 12 cos x
9sinx + 12cosx = 15 sin (x + 0.927)
max: 10 + 15 = 25
min: 10 - 15 = -5
Solve sin2x = -(1/2) for 0<=x<=360
The new range is 0<=2x<=720
Draw sinx to get the values 210, 330, 570, 690
Divide these values by 2 to get the solutions for sinx. Which are 105, 165, 285, 345
