Trigonometry SIMPLE

EQUATION

Trigonomentri simple equation

is an equation that contains the

comparison trigonomentri

In general, to solve trigonometry is used in the

following formula:

1. sin x = sin α

x = α + k.360⁰ atau x = (180⁰ - α) + k.360⁰

2. cos x = cos α

x = α + k.360⁰ atau x = - α + k.360⁰

3. tan x = tan α

x = α + k.180⁰

For angle in units of radians, in use the following formula:

1. sin x = sin α

x = α + k.2π or x = (π – α) + k.2π

2. cos x = sin α

x = α + k.2π or x = -α + k.2π

3. tan x = tan α

x = α + k.π

Example - example problems trigonometric

equations:

Determine the set of equations following the completion of the interval 0 ≤ x ≤ 2π

a. Sin x = ½ √3

b. Tan x = √3

Answer :

a. Sin x = ½√3

= sin (π/3 + k. 2π)

x = π/3 + k. 2π

for k = 0 x = π/3

OR

sin x = ½ √3

= sin ( π – π/3 + k. 2π)

x = 2π/3 + k . 2π

For k = 0 x = 2π/3

Thus, the solution set

= {π / 3, 2π / 3}

tan x = √3

= tan (π/3 + k. π )

x = π/3 + k . π

For k = 0 x = π/3 + k . Π

k = 1 x = 4π/3

so, the solution set

= {Π / 3, 4π / 3}

2. Determine the set of completion of the equation cos (3x - 45 ⁰) = - ½ √ 2, for 0 ⁰ ≤ x ≤ 360 ⁰.

Answer :

Cos (3x – 45⁰) = -½√2

Cos (3x – 45⁰) = cos 135⁰

3x – 45⁰ = 135⁰ + k. 360⁰

3x = 180⁰ + k. 360⁰

x = 60⁰ + k. 120⁰

x = 60⁰ , 180⁰ , 300⁰

OR

3x – 45⁰ = -135 + k . 360⁰

3x = -90⁰ + k . 360⁰

x = -30⁰ + k . 120⁰

x = 90⁰ , 210⁰ , 330⁰

Thus, the solution set = {60 ⁰, 90 ⁰, 180 ⁰, 210 ⁰, 300 ⁰, 330 ⁰}

The basic technique is to solve

trigonometric equations using trig identities and algebra techniques to transform a trigonometric equation into simpler forms.

example:

Determine the set of completion of sin x = sin 70°, 0° <x <360 °

Answer :

x = 70° + k.360° k = 0 ==> x = 70° atau

x = (180 - 70) + k.360° ==> x = 110° + k.360°

k = 0 ==> x = 110°

Jadi, Hp = {70°, 110°}

Determine the set of completion of cos x = cos 24 in the interval 0 ° <x <360 °

Answer :

x = 24° + k.360° k = 0 , x = 24° OR

x = -24° + k.360°

k = 1 , x = -24° + 360° = 336°

Thus, Hp = {24°, 336°}

Determine the set of completion of tan x = tan 56 °, in the interval 0 ° <x

<360 °

Answer:

x = 56 ° + ° k.180

k = 0 ==> x = 56 °

k = 1 ==> x = 56 ° + 180 ° = 236 °

Thus, the solution set is

{52 °, 236 °}

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