Cos,Tan,Sin equations

  • #1

Homework Statement



Please help solve these two equations (giving two solutions)

sin x =√ 2 cos x

sin^2 x - cos^2 x - 2sin x = 1


Any help no matter how little is much appreciated





Homework Equations





The Attempt at a Solution



Not sure how to solve these,

thanks in advance
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
When solving these types of equations, one method is to try and use trigonometric identities to manupulate the equations so that only one type of trigonometric function is left.

For example, with the first one, what could you divide both sides by so that there is only sin, cos or tan left over?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
965

Homework Statement



Please help solve these two equations (giving two solutions)

sin x =√ 2 cos x
[tex]\frac{sin x}{cos x}= tan x= \sqrt{2}[/tex]
Can you solve that?

sin^2 x - cos^2 x - 2sin x = 1
Since [itex]sin^2 x+ cos^2 x= 1[/itex], [itex]cos^2 x= 1- sin^2 x[/itex] so this becomes
[tex]sin^2 x- (1- sin^2 x)- 2 sin x= sin^2 x- 1+ sin^2 x- 2sin x= 1[/tex]
[tex]2sin^2 x- 2sin x- 2= 0[/tex]
[tex]sin^2 x- sin x- 1= 0[/tex]

Let y= sin x so the equation becomes [itex]y^2- y- 1= 0[/itex].


Any help no matter how little is much appreciated





Homework Equations





The Attempt at a Solution



Not sure how to solve these,

thanks in advance
 

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