- #26

- 581

- 20

Sin 2x = ## \frac{ -\sqrt2}{2}##

So 2x = 45/36 phi, 63/36 phi?

X = 45/72 phi or x = 63/72 phi

While x must on 4th quadrant..

Both x above not on 4th Q ..

What's wrong ?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Helly123
- Start date

- #26

- 581

- 20

Sin 2x = ## \frac{ -\sqrt2}{2}##

So 2x = 45/36 phi, 63/36 phi?

X = 45/72 phi or x = 63/72 phi

While x must on 4th quadrant..

Both x above not on 4th Q ..

What's wrong ?

- #27

SammyS

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

- 11,369

- 1,035

You can reduce those fractions. 45/36 = 5/4, etc., and it's pi, not phi.

Sin 2x = ## \frac{ -\sqrt2}{2}##

So 2x = 45/36 phi, 63/36 phi?

X = 45/72 phi or x = 63/72 phi

While x must on 4th quadrant..

Both x above not on 4th Q ..

What's wrong ?

More to the point for your question here:

In the problem statement the requirement is, 0 ≤ x < 2π . (Actually it has θ, not x. That's not important.)

Therefore, 0 ≤ 2x < 4π. Right?

So find the additional solutions which fit that. (Add 2π to those two answers you have for 2x .)

By The Way:

In the blue strip above the box in which you compose posts, there is a large ∑ character. Click on that to find a large set of characters useful for math/science.

θ π φ ∅ ℝ etc.

Last edited:

- #28

- 581

- 20

X 1=5/4 π

X2 = 7/4 π

Both added 2π to get x at 8 quadrants

X1 = 13/4 π

X2 = 15/4 π

Both satisfied the domain

How to decide which one is the answer?

- #29

- 581

- 20

I'm confused, why cos 13/4 π is negative, even though 13/4 π on 8 quadrants?

- #30

Ray Vickson

Science Advisor

Homework Helper

Dearly Missed

- 10,706

- 1,722

Sin 2x = ## \frac{ -\sqrt2}{2}##

So 2x = 45/36 phi, 63/36 phi?

X = 45/72 phi or x = 63/72 phi

While x must on 4th quadrant..

Both x above not on 4th Q ..

What's wrong ?

Because of "circularity", we have:

1st quadrant ↔ 5th quandrant ↔ 9th quandrant, etc.

4th quadrant ↔ 8th quadrant ↔ 12th quadrant, etc.

(Here, ↔ means "geometrically equivalent".)

Get it? The are only

- #31

SammyS

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

- 11,369

- 1,035

Those actually should written be something like

X 1=5/4 π

X2 = 7/4 π

Both added 2π to get x at 8 quadrants

X1 = 13/4 π

X2 = 15/4 π

Both satisfied the domain

How to decide which one is the answer?

2x_{1} = (5/4) π

2x_{2} = (7/4) π

Then adding 2π gives (two new possibilities for x):2x

2x_{3} = (13/4) π

2x_{4} = (15/4) π

2x

Solve for each x

Share: