Angle Ratios: Solving for θ between 0 and 360°

[chocolatelover]

Hi,

Homework Statement

Find every angle θ between 0 and 360° for which the ratio of sin θ to cos θ is -3.00. (Round your answer to the nearest degree.)

Homework Equations

The Attempt at a Solution

I used the unit circle and took the x value divided by the y value and none of them were -3. Is that how you would do it?

thank you very much

 

[rock.freak667]

the ratio of sin to cos is the same as $\frac{sin\theta}{cos\theta}$

Do you know any other trig identity that is the same as that?

 

[chocolatelover]

Thank you very much

That's the same thing as tangent, right? So, I just need to find out which tangent of a degree between 0 and 360 is -3, right? I tried that and everything is either 1 or a decimal number.

Thank you

 

[rock.freak667]

Yes it is the same as tan$\theta$

Well arctan(3) is a decimal number so just approximate the value.

 

[chocolatelover]

But it has to be equal to 3, right? You could also use Arctan?

Thank you

 

[rock.freak667]

In which quadrants is tan negative? Then the acute angle is arctan(3).

 

[chocolatelover]

Thank you very much

The arctan(3)=1.249. Could you please explain to me how I could find the smallest one and the largest one?

Thank you

 

[rock.freak667]

arctan(3) is the acute angle (A) that lies in the first quadrant. Tan is negative in the 2nd and fourth quadrant. How do you think you would find the angle made by something in the 2nd quadrant?(Hint: the sum of the angles at a point on a straight line is 190)

 

[chocolatelover]

Thank you very much

Isn't 180? So, wouldn't you take 180-1.249?

So the largest angle would be 178.751 and the smallest would be 1.249?

Thank you

 

[rock.freak667]

Thank you very much

Isn't 180? So, wouldn't you take 180-1.249?

So the largest angle would be 178.751 and the smallest would be 1.249?

Thank you

1.249 is radians,180 is in degrees...

180 degrees is equivalent to pi radians.

So you would take $\pi -1.249$

 

[chocolatelover]

Thank you

So, in degrees it would be 71.565 or 72 and 108.435 or 108, right?

Thank you very much

 

[rock.freak667]

Thank you

So, in degrees it would be 71.565 or 72 and 108.435 or 108, right?

Thank you very much

108.435 would be one answer.

The other answer is in quadrant 4. How would you find the angle made by something in the 4th quadrant? (measuring the angle anti-clockwise and the sum of the angles in a circle is 360)

 

[chocolatelover]

Would you just take 360-108?

 

[rock.freak667]

Would you just take 360-108?

You would take 360-arctan(3)

 

[chocolatelover]

Thank you very much

Regards