Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?
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Transcript of Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?
![Page 1: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/1.jpg)
Solving Trigonometric Equations
Sec. 5.1bHW: p. 456 39-67 odd
![Page 2: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/2.jpg)
Let’s start with a problem…
Solve
3coscot
sin
xx
x in the interval 0,2
3cos cos
sin sin
x x
x x
3cos cosx x3cos cos 0x x
2cos cos 1 0x x
2cos sin 0x x
cos 0x or sin 0x Reject sin(x) = 0…why???
3,2 2
x
So where is
0,2cos 0x
in ?
![Page 3: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/3.jpg)
Solving a Trig. Eq. by Factoring
Find all solutions to the equation 22sin sin 1x x Let sinu x
Substitute: 22 1u u 22 1 0u u
2 1 1 0u u 2 1 0u or 1 0u 1
2u or 1u
1sin
2x or sin 1x
![Page 4: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/4.jpg)
Solving a Trig. Eq. by Factoring
Find all solutions to the equation 22sin sin 1x x First, find thesolutions in the interval
1sin
2x or sin 1x 0,2
5,6 6
x
3
2x
To get all real solutions, simply add integer multiples of the period:
26
x n or
52
6x n
or3
22
x n
0, 1, 2,n
![Page 5: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/5.jpg)
Solving a Trig. Eq. with a Calculator
Find all solutions to the equation , using a calculatorwhere needed.
cos 0.7t
0.795t To get all real solutions, simply add integer multiples of the period:
0.795 2t n 0, 1, 2,n
Find the solutions in the interval by graphing: ,
![Page 6: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/6.jpg)
Guided PracticeFind all solutions to the given equation in the interval .Do not use a calculator.
Factor:
2 tan cos tan 0x x x tan 2 cos 1 0x x
0,2
tan 0x or1
cos2
x
0,x 7,4 4
x
Final Answer:7
0, , ,4 4
x
![Page 7: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/7.jpg)
Guided PracticeFind all solutions to the given equation in the interval .Do not use a calculator.
2sin tan sinx x x
0,2
2sin tan sin 0x x x 2sin tan 1 0x x
sin 0x or 2tan 1x
0,x 3 5 7, , ,4 4 4 4
x
Final Answer:3 5 7
0, , , , ,4 4 4 4
x
![Page 8: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/8.jpg)
Guided PracticeFind all solutions to the given equation. Do not use a calculator.
22sin 3sin 1 0x x 2sin 1 sin 1 0x x
1sin
2x 7 3 11
, ,6 2 6
x
Initial answers:
Final Answers:
7 3 112 , 2 , 2
6 2 6x n n n
(n an integer)
or sin 1x
![Page 9: Sec. 5.1b HW: p. 456 39-67 odd. Solvein the interval or Reject sin(x) = 0…why??? So where is in ?](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649f335503460f94c50954/html5/thumbnails/9.jpg)
Guided PracticeFind all solutions to the given equation. Do not use a calculator.
23sin 2cost t 23sin 2 2sint t
Final Answers:5
2 , 26 6
t n n
(n an integer)
1sin
2t or sin 2t Can the sine of an
angle ever equal –2???5,6 6
t
Initial answers:
22sin 3sin 2 0t t 2sin 1 sin 2 0t t