Solve a Trig Equation Containing secant

  • Thread starter nickb145
  • Start date
  • #1
68
0

Homework Statement



sec(5x)-5=0

Homework Equations





The Attempt at a Solution




I turned it into 1/cos(5x)=5 x=θ/5
then i switched it to cos(5x)=/1/5

Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution
since the positive cos is in the 1st and 4th quadrant i need to subtract 2pi to 1.36= 4.91 then divide by 5 which gives me .9827 which also works

But i am stuck after that
 
Last edited:

Answers and Replies

  • #2
35,231
7,053

Homework Statement



sec(5x)-5=0

Homework Equations





The Attempt at a Solution




I turned it into 1/cos(5x)=5 x=θ/5
then i switched it to cos(5x)/1/5
And lost your equation.

You're making this harder than it needs to be. If 1/cos(5x) = 5, then cos(5x) = 1/5.

You could also say that cos(5x + k*2##\pi##) = 1/5, and since cosine is positive in Q IV, you could also say that cos(-5x + k*2##\pi##) = 1/5, where k is an integer.

Now you can take cos-1 of both sides.
Then cos-1(1/5)=θ which = 1.36 (one solution) then divided by 5 which is .2738 which works as one solution
since the positive cos is in the 1st and 4th quadrant i need to subtract 2pi to 1.36= 4.91 then divide by 5 which gives me .9827 which also works

But i am stuck after that
 

Related Threads on Solve a Trig Equation Containing secant

  • Last Post
Replies
8
Views
8K
  • Last Post
Replies
10
Views
4K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
35K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
24
Views
5K
Replies
2
Views
1K
  • Last Post
Replies
8
Views
2K
Top