Transcript General Solutions to Trigonometric Equations

General Solutions to Trigonometric
Equations
Lesson 5.7
Definitions
• Trigonometric equations :
WATCH OUT FOR THE DOMAIN!
FIGURE OUT IF YOU ARE IN DEGREES OR
RADIANS!!
Example 1
• Consider the equation cos x = .456
– Estimate the solution between 0 and π to the
nearest thousandth
1.097
– Estimate all solutions between 0 and 2π.
1.097, 5.186
- Describe all real solutions.
1.097 + 2πn, 5.186+ 2πn


 x  80 
y

12
.
25
Example 2

 sin 
3.75
 365 


 2 
This estimates the number of hours y of daylight
on the xth day of the year at the latitude of
Seattle. Approximately when is a daylight
period 11 hours long in Seattle?
1
 x  80 2 
  sin 


3
365 
 1
 .33984  .0172x 1.3771
3.4814  .0172x 1.3771
1
  sin(. 0172 x  1.3771)
3
282.47, 60.3  x
Example 3
Solve for x in degrees:
2
3 tan x + 4tan x + 1 = 0
(3tanx + 1) (tan x + 1) = 0
3 tan x + 1 = 0
tan x + 1 = 0
tan x = -1/3
tan x = -1
x = 341.6 + 360n
x = 135 + 360n
161.6 + 360n
x = 315 + 360n
Homework
Pages 351 – 352
7 - 14, 19, 21
Skip 11 b.