how to find (theta) so that cos (theta) = 1/2

[abel muroi]

when a problem asks you to find "theta"..

does that mean that they want you to find the angle (in degrees) that has an adjacent of Y and the hypotenuse of X?

 

[Steven G]

when a problem asks you to find "theta"..

does that mean that they want you to find the angle (in degrees) that has an adjacent of Y and the hypotenuse of X?

Yes, you take cos, sin, tan...of angles. If the angle is called theta than yes the angle is theta.

I am not sure what you mean by x and y. If the cos(theta) = 1/2 than the ratio of the side adjacent to theta to the hypotenuse is 2. You can simply say that the side adjacent to theta has length 1 and the hypotenuse has length 2.

And no you do not have to find theta in degrees, as you can find it in radians unless the problem specifically says to find theta in degrees (or theta).
So how do you find theta? What does theta equal?

 

[abel muroi]

Yes, you take cos, sin, tan...of angles. If the angle is called theta than yes the angle is theta.

I am not sure what you mean by x and y. If the cos(theta) = 1/2 than the ratio of the side adjacent to theta to the hypotenuse is 2. You can simply say that the side adjacent to theta has length 1 and the hypotenuse has length 2.

And no you do not have to find theta in degrees, as you can find it in radians unless the problem specifically says to find theta in degrees (or theta).
So how do you find theta? What does theta equal?

By X and Y i really meant any value.

ok I'll show you the work that I have done..

cos(theta) = 1/2
1/2 = 0.5
cos^-1 (0.5) = 60 degrees

theta = 60

i used a calculator and got 60 degrees as a result.

so is that how you find theta?

 

[Steven G]

By X and Y i really meant any value.

ok I'll show you the work that I have done..

cos(theta) = 1/2
1/2 = 0.5
cos^-1 (0.5) = 60 degrees

theta = 60

i used a calculator and got 60 degrees as a result.

so is that how you find theta?

Correct. Instead of writing cos^-1 (0.5) = 60 degrees I would have written theta = cos^-1 (0.5) = 60 degrees
Good job

 

[HallsofIvy]

You shouldn't need to use a calculator.

Draw an equilateral triangle with sides of length 2. Then all three angles are 60 degrees (pi/3 radians). The altitude from one vertex to the opposite side is perpendicular to that side and bisects the side. That means we have a right triangle with one angle 60 degrees, hypotenuse of length 2, and "near side" of length 1/2. Therefore, cos(60)= 1/2.

(Since you are using "60 degrees" rather than "pi/2 radians", I assume you have not extended the trig functions to all real numbers and so do not have to give other values of theta that also have cosine equal to 1/2.)

 

[abel muroi]

You shouldn't need to use a calculator.

Draw an equilateral triangle with sides of length 2. Then all three angles are 60 degrees (pi/3 radians). The altitude from one vertex to the opposite side is perpendicular to that side and bisects the side. That means we have a right triangle with one angle 60 degrees, hypotenuse of length 2, and "near side" of length 1/2. Therefore, cos(60)= 1/2.

(Since you are using "60 degrees" rather than "pi/2 radians", I assume you have not extended the trig functions to all real numbers and so do not have to give other values of theta that also have cosine equal to 1/2.)

HallsofIvy, how can i find the angle (in degrees) of a triangle without using a calculator?

 

[stapel]

HallsofIvy, how can i find the angle (in degrees) of a triangle without using a calculator?

That will depend upon the angle. If it's a reference angle, or something that can be related (via identities) to these basic (and memorized) angles, then you'll use that. Otherwise, you'd probably have to use tables.