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SUEC 高中 Adv Maths (Trigo Equation) (Part 3)
- 1. 𝒑𝒈 𝟐𝟖𝟒
- 2. 𝒑𝒈 𝟐𝟖𝟔 − 150 ° , −110 ° , 10 ° , 130 ° − 10.1 °, −169.9 ° 0, 1 9 𝜋, 2 5 𝜋, 1 3 𝜋, 5 9 𝜋, 7 9 𝜋, 4 5 𝜋, 𝜋 𝑥 = 0 °, 120 °, 180 °
- 3. 𝒑𝒈 𝟐𝟖𝟒
- 4. 𝒑𝒈 𝟐𝟖𝟒 − 𝟐𝟖𝟓 𝒆𝒗𝒆𝒏 𝒐𝒅𝒅
- 5. 𝒑𝒈 𝟐𝟖𝟓
- 6. 𝒑𝒈 𝟐𝟖𝟔 𝟐𝒏𝝅 + 𝝅 𝟐 𝟐𝒏𝝅 𝟐𝒏𝝅 ± 𝟐𝝅 𝟑 𝒏𝝅 + −𝟏 𝒏 𝝅 𝟔 𝒏𝝅 + 𝝅 𝟐
- 7. 𝒑𝒈 𝟐𝟖𝟔 𝒙 = 𝟐𝒏𝝅 + 𝝅 𝟐 𝒙 = 𝟐𝒏𝝅 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 − 𝑠𝑖𝑛 𝑥 − (𝑐𝑜𝑠 𝑥 − 1) = 0 𝑠𝑖𝑛 𝑥 (𝑐𝑜𝑠 𝑥 − 1) − (𝑐𝑜𝑠 𝑥 − 1) = 0 (𝑐𝑜𝑠 𝑥 − 1) (𝑠𝑖𝑛 𝑥 − 1) = 0 𝑐𝑜𝑠 𝑥 − 1 = 0 𝑜𝑟 𝑠𝑖𝑛 𝑥 − 1 = 0 𝑐𝑜𝑠 𝑥 = 1 𝑠𝑖𝑛 𝑥 = 1
- 8. 𝒑𝒈 𝟐𝟖𝟔 (𝟒𝒏 − 𝟏) 𝝅 𝟔 𝟐𝒏𝝅 𝟐𝒏𝝅 ± 𝟑𝝅 𝟒 𝒏𝝅 + 𝝅 𝟐 𝟐𝒏𝝅 ± 𝝅 𝟔 𝟐𝒏𝝅 𝟑 ± 𝟐𝝅 𝟗 𝒏𝝅 𝟓 + 𝝅 𝟏𝟎 − 𝟏 𝒏𝝅 𝟐 − 𝟏
- 9. 𝒑𝒈 𝟐𝟖𝟔 𝒙 = 𝒏𝝅 𝟓 + 𝝅 𝟏𝟎 − 𝟏 𝒙 = 𝒏𝝅 𝟐 − 𝟏 𝐿𝑒𝑡 (𝑥 + 1) = 𝛼 𝑠𝑖𝑛 𝛼 𝑐𝑜𝑠 2𝛼 = 𝑠𝑖𝑛 3𝛼 𝑐𝑜𝑠 4𝛼 1 2 (𝑠𝑖𝑛 3𝛼 + 𝑐𝑜𝑠 𝛼) = 1 2 (𝑠𝑖𝑛 7𝛼 + 𝑐𝑜𝑠 𝛼) 𝑠𝑖𝑛 7𝛼 − 𝑠𝑖𝑛 3𝛼 = 0 2 𝑐𝑜𝑠 5𝛼 𝑠𝑖𝑛 2𝛼 = 0 𝑐𝑜𝑠 5𝛼 = 0 𝑜𝑟 𝑠𝑖𝑛 2𝛼 = 0 5𝛼 = 𝑛𝜋 + 𝜋 2 2𝛼 = 𝑛𝜋 𝑥 + 1 = 𝑛𝜋 5 + 𝜋 10 𝑥 + 1 = 𝑛𝜋 2
- 10. 𝒑𝒈 𝟐𝟖𝟔 𝒏𝝅 𝟐𝒏𝝅 ± 𝝅 𝟒 𝒏𝝅 + 𝝅 𝟐 𝟐𝒏𝝅 ± 𝟑𝝅 𝟒 𝒏𝝅 + −𝟏 𝒏 − 𝝅 𝟔 𝒏𝝅 𝟐𝒏𝝅 ± 𝝅 𝟑 𝟐𝒏𝝅 ± 𝟐𝝅 𝟑
- 11. 𝒑𝒈 𝟐𝟖𝟔 𝒙 = 𝒏𝝅 𝒙 = 𝟐𝒏𝝅 ± 𝝅 𝟒 2 𝑠𝑖𝑛2 𝑥 − 2 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 2 = 0 2 𝑠𝑖𝑛2 𝑥 (1 − 2 𝑐𝑜𝑠2 𝑥) = 0 𝑠𝑖𝑛 𝑥 = 0 𝑜𝑟 𝑐𝑜𝑠 𝑥 = 1 2 𝒏𝝅 𝟐𝒏𝝅 ± 𝝅 𝟑 𝟐𝒏𝝅 ± 𝟐𝝅 𝟑
- 12. 𝒑𝒈 𝟐𝟖𝟔 2𝒏𝝅 𝟐 𝟗 𝒏𝝅 + 𝝅 𝟗 𝒏𝝅 + 𝝅 𝟐 𝒏𝝅 𝟒
- 13. 𝒑𝒈 𝟐𝟖𝟔 2 𝑐𝑜𝑠 2𝑥 𝑐𝑜𝑠 𝑥 = 2 𝑐𝑜𝑠 6𝑥 𝑐𝑜𝑠 𝑥 2 𝑐𝑜𝑠 𝑥 (𝑐𝑜𝑠 6𝑥 − 𝑐𝑜𝑠 2𝑥) = 0 2 𝑐𝑜𝑠 𝑥 (− 2 𝑠𝑖𝑛 4𝑥 𝑠𝑖𝑛 2𝑥) = 0 𝑠𝑖𝑛 4𝑥 = 0 𝑜𝑟 𝑠𝑖𝑛 2𝑥 = 0 4𝑥 = 𝑛𝜋 2𝑥 = 𝑛𝜋 𝒙 = 𝒏𝝅 + 𝝅 𝟐 𝒙 = 𝒏𝝅 𝟒 𝒙 = 𝒏𝝅 𝟐 𝑐𝑜𝑠 𝑥 = 0
- 14. 𝒑𝒈 𝟐𝟖𝟔
- 16. 𝒑𝒈 𝟐𝟖𝟕 An equation is called a homogeneous equation in sin and cos, if and only if all its terms are of the same degree in sin and cos of the same angle. To solve the homogeneous equation it is necessary: a) to transfer all terms to the left-hand side; b) to take all common factors out of brackets; c) to equate all factors and brackets to zero; d) the brackets equated to zero give the homogeneous equation of the smaller degree, which should be divided by cos ( or sin ) of the higher power; e) to solve the received algebraic equation in tan .
- 17. 𝒑𝒈 𝟐𝟖𝟕
- 18. 𝒑𝒈 𝟐𝟖𝟕
- 19. 𝒑𝒈 𝟐𝟖𝟕 − 𝟐𝟖𝟖
- 20. 𝒑𝒈 𝟐𝟖𝟖 𝒏𝝅 + 𝟔𝟑 ° 𝟐𝟔’ 𝒏𝝅 ± 𝝅 𝟒 𝒏𝝅 + 𝟓𝟔 ° 𝟏𝟗’ 𝒏𝝅 − 𝟒𝟓 ° 𝒏𝝅 + 𝟕𝟏 ° 𝟑𝟒’ 𝒏𝝅 − 𝟒𝟓 ° 𝒏𝝅 + 𝟓𝟗 ° 𝟐’ 𝒏𝝅 + 𝟓𝟔 ° 𝟏𝟗’ 𝒏𝝅 − 𝟑𝟑 ° 𝟒𝟏’ 𝒏𝝅 + 𝟏𝟒 ° 𝟐’ 𝒏𝝅 + 𝟕𝟏 ° 𝟑𝟒’ 𝒏𝝅 + 𝟒𝟓 ° 𝒏𝝅 + 𝟐𝟔 ° 𝟑𝟓’ 𝒏𝝅 + 𝟗𝟎 ° 𝒏𝝅 + 𝟐𝟔 ° 𝟑𝟒’
Editor's Notes
- 4. sin x = cos (90-x) 90-x = 2x+60
- divide 2
- http://www.bymath.com/studyguide/tri/sec/tri16.htm http://www.nabla.hr/TF-TrigFunEquA6.htm#The%20basic%20strategy%20for%20solving%20trigonometric%20equations