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Презентация, доклад по математике Квадратные тригонометрические уравнения и неравенства
Содержание
- 1. Презентация по математике Квадратные тригонометрические уравнения и неравенства
- 2. Square rooting:orThe original problem has become 2
- 3. 1st solution: 1st solution:
- 4. The original problem has become 2 simple
- 5. Principal value: This is easy! We can just use the sketch.
- 6. 1-1This is easy! We can just use the sketch. Principal value:
- 7. This is easy! We can just use the sketch. Principal value:
- 8. e.g. 3 Solve the equation
- 9. Principal Solution:
- 10. Ans: Ans:
- 11. The formula we use is sometimes called
- 12. Proof of the Pythagorean Identity.Using Pythagoras’ theorem:Consider the right angled triangle ABC.
- 13. Identity symbols are normally only used when
- 14. Solution:
- 15. Слайд 15
- 16. We just look at the graph!
- 17. Consider the right angled triangle ABC.
- 18. We now have one simple trig equation.
- 19. Слайд 19
- 20. SUMMARY Replace the ratio by c, s
- 21. Solve the equation for
- 22. Solve the equation for
- 23. Слайд 23
- 24. Solution:
Square rooting:orThe original problem has become 2 simple trig equations, so we solve in the usual way.
Слайд 2Square rooting:
or
The original problem has become 2 simple trig equations, so
we solve in the usual way.
Слайд 4The original problem has become 2 simple trig equations, so we
again solve in the usual way.
This is a quadratic equation, so it has 2 solutions.
Common factor:
( Method: Try to factorise; if there are no factors, use the formula or complete the square. )
Слайд 11The formula we use is sometimes called the Pythagorean Identity and
we will prove it now.
. . . we need a formula that will change one of these trig ratios into a function of the other.
Слайд 12Proof of the Pythagorean Identity.
Using Pythagoras’ theorem:
Consider the right angled triangle
ABC.
Слайд 13Identity symbols are normally only used when we want to stress
that we have an identity. In the trig equations we use an = sign.
Слайд 20SUMMARY
Replace the ratio by c, s or t as appropriate.
Collect
the terms with zero on one side of the equation.
Factorise the quadratic and solve the resulting 2 trig equations.
or
if there are no squared terms.
