Post on 20-Jan-2016
description
Trig Equations
LO: Solve basic trignometric equations
Sine Function y=sinx
−90 90 180 270 360
−2
−1
1
2
x
y
Cosine Function y=cosx
−90 90 180 270 360
−2
−1
1
2
x
y
Tangent Function y=tanx
−90 90 180 270 360
−2
−1
1
2
x
y
Review on Radians
90 =
180 =
270 =
360 =
2
2
2
3
Sine Function
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
Cosine Function
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
Tangent Function
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
Vocabulary
Domain: set of possible x- values Range: set of possible y- values Period: Minimum interval of which the
function repeats itself Height of the wave function.
Key Featuresy=sinx y=cosx y=tanx
Period 360 degrees 360 degrees
180 degrees
Amplitude 1 1 NA
Asymptote NA NA -90, 90, 270 etc
Domain Except for asymptotes
Range
x xx
y y y
Solving Trig Equations
2
12sin x
−90 90 180 270 360
−2
−1
1
2
x
y
for 3600 x
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
2
12sin x for 20 x
Trig Functions can also transform..
dcbxay )cos(Change amplitude
Change period + Moves left
- Moves right+ Moves up
- Moves down
Your turn853.0)70cos(5 x
for20 x
3600 xa
b
−90 90 180 270 360
−2
−1
1
2
x
y
169.8 330.2
Your turn853.0)70cos(5 x
for20 x
3600 xa
b
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
2.63 5.43
How to do it using symmetry..
Solve for 0 < x 360
cos x = 0.12
x = cos 0.12
x = 83.1
or
x = 360 – 83.1
x = 276.9
1
−90 90 180 270 360
−2
−1
1
2
x
y
83.1 360 – 83.1
Find x when sin x=0.46
sin x = 0.46
x = sin 0.46
x = 0.478 radians
or
x= – 0.478
x=2.664 rads
20 x
1
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
0.478 -0.478
Rearrangements.
Solve for x in the domain
2 cos x = 0.5
cos x = 0.25 [dividing each side by 2]
x = cos 0.25
x = 75.5
3600 x
1
−90 90 180 270 360
−2
−1
1
2
x
y
75.5 360 - 75.5
Solve for x in the domain of 20 x
Solve for x in the domain
2 tan (x) + 3 = 4.5
2 tan (x) = 4.5 - 3
tan (x) = 0.75 [diving by 2]
x = tan 0.75
x = 0.634
1
−π/2 π/2 π 3π/2 2π
−2
−1
1
2
x
y
0.643 + 0.643