The document discusses solving trigonometric equations by using trigonometric identities and algebra techniques to transform the equations into simpler forms. It provides examples of determining the set of solutions for trigonometric equations in a given interval by using formulas for sine, cosine, and tangent. Solutions are found by setting the trigonometric functions equal to each other and solving the resulting equations.

1. Trigonometry SIMPLE
EQUATION

2. Trigonomentri simple
equation
is an equation that contains the
comparison trigonomentri

3. In general, to solve
trigonometry is used in the
following formula:

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

5. 2. cos x = cos α
x = α + k.360⁰ atau x = - α + k.360⁰

6. 3. tan x = tan α
x = α + k.180⁰

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

8. 1. sin x = sin α
x = α + k.2π or x = (π – α) + k.2π

9. 2. cos x = sin α
x = α + k.2π or x = -α + k.2π

10. 3. tan x = tan α
x = α + k.π

11. Example - example
problems trigonometric
equations:

12.  Determine the set of
equations following the
completion of the interval
0 ≤ x ≤ 2π
a. Sin x = ½ √3
b. Tan x = √3

13. Answer :
a. Sin x = ½√3
= sin (π/3 + k. 2π)
x = π/3 + k. 2π
for k = 0 x = π/3

14. OR
sin x = ½ √3
= sin ( π – π/3 + k.
2π)
x = 2π/3 + k . 2π
For k = 0 x = 2π/3

15. Thus, the solution set
= {π / 3, 2π / 3}

16. 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

17. so, the solution set
= {Π / 3, 4π / 3}

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

19. 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

20. OR
3x – 45⁰ = -135 + k . 360⁰
3x = -90⁰ + k . 360⁰
x = -30⁰ + k . 120⁰
x = 90⁰ , 210⁰ , 330⁰

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

22. The basic technique is to solve
trigonometric equations using trig
identities and algebra techniques to
transform a trigonometric equation into
simpler forms.

23. example:
Determine the set of
completion of sin x = sin 70°,
0° <x <360 °

24. 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°}

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

26. Answer :
x = 24° + k.360°
k = 0 , x = 24° OR
x = -24° + k.360°
k = 1 , x = -24° + 360° = 336°
Thus, Hp = {24°, 336°}

27. Determine the set of completion of tan
x = tan 56 °, in the interval 0 ° <x
<360 °

28. Answer:
x = 56 ° + ° k.180
k = 0 ==> x = 56 °
k = 1 ==> x = 56 ° + 180 ° = 236 °
Thus, the solution set is
{52 °, 236 °}

29. THANK YOU