Unit circle questions (2 Viewers)

[capper]

Could anyone please show me how to do these questions

1. sinx=cosx
2. 2sinx + cosx =0
3. tan x= 2sinx
4. cotx = 2cosx
5. sin2x =tanx

Thanks

 

[Drongoski]

What have these questions to do with the "unit circle?

 

[hayabusaboston]

Could anyone please show me how to do these questions

1. sinx=cosx
2. 2sinx + cosx =0
3. tan x= 2sinx
4. cotx = 2cosx
5. sin2x =tanx

Thanks

JEez capper im not exactly sure you learned anything from my and Carrotsticks answers....

 

[cutemouse]

What have these questions to do with the "unit circle?

Because trigonometric identities can be derived from the unit circle.

Consider a unit circle x^2 + y^2 =1. If P(cos theta, sin theta) is a point on this unit circle then cos^2 theta + sin^2 theta = 1. Etc

 

[RivalryofTroll]

Could anyone please show me how to do these questions

1. sinx=cosx
2. 2sinx + cosx =0
3. tan x= 2sinx
4. cotx = 2cosx
5. sin2x =tanx

Thanks

1. sinx/cosx=1
tan x = 1
solve for x

2. 2sinx = -cosx
2 = -cotx
cotx = -2
tan x = -1/2
solve for x

3. sinx/cosx = 2sinx
sinx/cosx - 2sinxcosx/cosx = 0
sinx - 2sinxcosx = 0
sinx (1-2cosx) = 0
sinx = 0
cosx = 1/2
Solve for x

4. cosx/sinx = 2cosx
cosx - 2cosxsinx = 0
cosx (1-2sinx) = 0
cosx = 0
sinx = 1/2
Solve for x

5. sin2x = tanx
2sinxcosx = sinx/cosx
2sinxcos^2x/cosx - sinx/cosx = 0
2sinxcos^2x - sinx = 0
sinx (2cos^2x - 1) = 0
sinx (cos2x) = 0
Solve for x

Correct me if I got anything wrong. ):

 

[Carrotsticks]

Because trigonometric identities can be derived from the unit circle.

Consider a unit circle x^2 + y^2 =1. If P(cos theta, sin theta) is a point on this unit circle then cos^2 theta + sin^2 theta = 1. Etc

What you're saying implies that any trigonometry question is a 'unit circle' question.

 

[cutemouse]

What you're saying implies that any trigonometry question is a 'unit circle' question.

I was joking...

On a serious note, the op probably saw "unit circle" in the chapter of his/her textbook which contained these questions (for the reason I've outlined in my previous joke)...

 

[Carrotsticks]

I was joking...

On a serious note, the op probably saw "unit circle" in the chapter of his/her textbook which contained these questions (for the reason I've outlined in my previous joke)...

Then again, the Unit Circle is sort of like an axiom for all of Trigonometry.

Gotta love it.