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