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# Matematika - Persamaan Trigonometri Sederhana

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### Transcript

• 1. Trigonometry SIMPLE EQUATION
• 2. Trigonomentri simpleequation is an equation that contains thecomparison trigonomentri
• 3. In general, to solvetrigonometry is used in the following formula:
• 4. 1. sin x = sin &#x3B1; x = &#x3B1; + k.360&#x2070; atau x = (180&#x2070; - &#x3B1;) + k.360&#x2070;
• 5. 2. cos x = cos &#x3B1;x = &#x3B1; + k.360&#x2070; atau x = - &#x3B1; + k.360&#x2070;
• 6. 3. tan x = tan &#x3B1; x = &#x3B1; + k.180&#x2070;
• 7. For angle in units of radians, in use the following formula:
• 8. 1. sin x = sin &#x3B1; x = &#x3B1; + k.2&#x3C0; or x = (&#x3C0; &#x2013; &#x3B1;) + k.2&#x3C0;
• 9. 2. cos x = sin &#x3B1;x = &#x3B1; + k.2&#x3C0; or x = -&#x3B1; + k.2&#x3C0;
• 10. 3. tan x = tan &#x3B1; x = &#x3B1; + k.&#x3C0;
• 11. Example - exampleproblems trigonometric equations:
• 12. &#xF097; Determine the set of equations following the completion of the interval 0 &#x2264; x &#x2264; 2&#x3C0;a. Sin x = &#xBD; &#x221A;3b. Tan x = &#x221A;3
• 13. Answer :a. Sin x = &#xBD;&#x221A;3 = sin (&#x3C0;/3 + k. 2&#x3C0;) x = &#x3C0;/3 + k. 2&#x3C0; for k = 0 x = &#x3C0;/3
• 14. ORsin x = &#xBD; &#x221A;3 = sin ( &#x3C0; &#x2013; &#x3C0;/3 + k.2&#x3C0;) x = 2&#x3C0;/3 + k . 2&#x3C0; For k = 0 x = 2&#x3C0;/3
• 15. Thus, the solution set = {&#x3C0; / 3, 2&#x3C0; / 3}
• 16. tan x = &#x221A;3 = tan (&#x3C0;/3 + k. &#x3C0;) x = &#x3C0;/3 + k . &#x3C0;For k = 0 x = &#x3C0;/3 + k.&#x3A0; k=1 x = 4&#x3C0;/3
• 17. so, the solution set = {&#x3A0; / 3, 4&#x3C0; / 3}
• 18. 2. Determine the set of completion of the equation cos (3x - 45 &#x2070;) = - &#xBD; &#x221A; 2, for 0 &#x2070; &#x2264; x &#x2264; 360 &#x2070;.
• 19. Answer : Cos (3x &#x2013; 45&#x2070;) = -&#xBD;&#x221A;2 Cos (3x &#x2013; 45&#x2070;) = cos 135&#x2070; 3x &#x2013; 45&#x2070; = 135&#x2070; + k. 360&#x2070; 3x = 180&#x2070; + k. 360&#x2070; x = 60&#x2070; + k. 120&#x2070; x = 60&#x2070; , 180&#x2070; , 300&#x2070;
• 20. OR3x &#x2013; 45&#x2070; = -135 + k . 360&#x2070; 3x = -90&#x2070; + k . 360&#x2070; x = -30&#x2070; + k . 120&#x2070; x = 90&#x2070; , 210&#x2070; , 330&#x2070;
• 21. Thus, the solution set = {60 &#x2070;, 90 &#x2070;, 180 &#x2070;, 210 &#x2070;, 300 &#x2070;, 330 &#x2070;}
• 22. The basic technique is to solvetrigonometric equations using trigidentities and algebra techniques totransform a trigonometric equation intosimpler forms.
• 23. example:Determine the set ofcompletion of sin x = sin 70&#xB0;,0&#xB0; &lt;x &lt;360 &#xB0;
• 24. Answer : x = 70&#xB0; + k.360&#xB0; k = 0 ==&gt; x = 70&#xB0; atau x = (180 - 70) + k.360&#xB0; ==&gt; x=110&#xB0; + k.360&#xB0; k = 0 ==&gt; x = 110&#xB0; Jadi, Hp = {70&#xB0;, 110&#xB0;}
• 25. Determine the set ofcompletion of cos x = cos 24in the interval 0 &#xB0; &lt;x &lt;360 &#xB0;
• 26. Answer : x = 24&#xB0; + k.360&#xB0; k = 0 , x = 24&#xB0; OR x = -24&#xB0; + k.360&#xB0; k = 1 , x = -24&#xB0; + 360&#xB0; = 336&#xB0; Thus, Hp = {24&#xB0;, 336&#xB0;}
• 27. Determine the set of completion of tan x = tan 56 &#xB0;, in the interval 0 &#xB0; &lt;x &lt;360 &#xB0;
• 28. Answer: x = 56 &#xB0; + &#xB0; k.180 k = 0 ==&gt; x = 56 &#xB0; k = 1 ==&gt; x = 56 &#xB0; + 180 &#xB0; = 236 &#xB0; Thus, the solution set is {52 &#xB0;, 236 &#xB0;}
• 29. THANK YOU