1. ## Angles

Good day,hope I'm welcome

I'm having problem solving these

Find the circular functions of the following:

a. 36 deg
b. 22 deg and 30 minutes
c. 15 deg = ( 30 deg / 2 )

For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

Same goes for letter b.

And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

Hoping for replies.

Thanks

2. Originally Posted by ImKo
Good day,hope I'm welcome

I'm having problem solving these

Find the circular functions of the following:

a. 36 deg
b. 22 deg and 30 minutes
c. 15 deg = ( 30 deg / 2 )

For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

Same goes for letter b.

And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

...
I'm confused about what you are asked to calculate ... But maybe this helps a little bit further:

All the given values of the angles are integer parts of 360°:

$\displaystyle 36^\circ = \dfrac1{10} \cdot 360^\circ$

$\displaystyle 22^\circ 30' = \dfrac12 \cdot 45^\circ = \dfrac1{16} \cdot 360^\circ$

$\displaystyle 15^\circ = \dfrac1{24} \cdot 360^\circ$

3. Originally Posted by ImKo
Good day,hope I'm welcome

I'm having problem solving these

Find the circular functions of the following:

a. 36 deg
b. 22 deg and 30 minutes
c. 15 deg = ( 30 deg / 2 )

For a. I tried to find special angles(30,60,45,and other quadrantal angles) that would sum up to 36 deg , but I just can't find any.

Same goes for letter b.

And for letter c. I can't think of any procedure that will direct me to the correct answer, using 30 deg / 2.

Hoping for replies.

Thanks

Remember that a "radian" is the length of a radius on the circumference of a circle. Since it is the length of the radius on the CIRCUMFERENCE, it is given the symbol C.

$\displaystyle C = 2\pi r = 2\pi\times 1 = 2\pi^C$.

So there are $\displaystyle 2\pi$ radians in a circle.

Recall that there are also $\displaystyle 360^{\circ}$ in a circle.

So $\displaystyle 360^{\circ} = 2\pi^C$

So $\displaystyle 1^{\circ} = \frac{\pi}{180}^C$.

So to find the number of radians in a certain number of degrees, multiply by

$\displaystyle \frac{\pi}{180}$.

4. We are asked to find the

sine, cosine, tangent, cosecant, secant, cotangent of the following angles

like sin30 deg = 1/2.......etc

It would be best if it is in radical form

Hope it clears things.

Thanks for any help

5. Originally Posted by ImKo
We are asked to find the

sine, cosine, tangent, cosecant, secant, cotangent of the following angles

like sin30 deg = 1/2.......etc

It would be best if it is in radical form

Hope it clears things.

Thanks for any help
OK, in that case, for b) and c) you need to use the half angle formulas...

$\displaystyle \sin{\frac{\theta}{2}} = \pm \sqrt{\frac{1 - \cos{\theta}}{2}}$

$\displaystyle \cos{\frac{\theta}{2}} = \pm \sqrt{\frac{1 + \cos{\theta}}{2}}$

$\displaystyle \tan{\frac{\theta}{2}} = \frac{\sin{\theta}}{1 + \cos{\theta}}$.

6. Thanks I got the sin, cos, and the tan, already

So..........How do I get the sec, csc, cot ?

Should I get their reciprocals?

and when should I use these formulas?

tan y/2 = 1- cos y / sin y

tan y/2 = sin y / 1 + cos y

Thanks

7. Originally Posted by ImKo
Thanks I got the sin, cos, and the tan, already

So..........How do I get the sec, csc, cot ?

Should I get their reciprocals?

and when should I use these formulas?

tan y/2 = 1- cos y / sin y

tan y/2 = sin y / 1 + cos y

Thanks
Yes, once you've got sin, cos and tan, just take their reciprocals and you have the csc, sec and cot.

As for the tan formulae, you wanted to find $\displaystyle \tan{22^{\circ}30'} = \tan{\frac{45^{\circ}}{2}}$ and $\displaystyle \tan{15^{\circ}} = \tan{\frac{30^{\circ}}{2}}$ didn't you?

8. Never mind my other question. I had an error there

My question was supposed to be

"when should I use these identities

tan^2 y /2 = 1 - cos y / 1 + cos y
tan y /2 = 1 - cos y / sin y
tan y /2 = sin y / 1 + cos y

since they are all Tangent-Half-Measure Identities" I was thinking they are all of different uses

Later on I found out they are all just equal, After some computations

As for letter a. how should I solve it?

Anyway thanks for the help!

And HAPPY NEW YEAR TO ALL, its December 31, 2008 here waiting for the New Year to come 1 hour or so from now its already 2009!!