Pre-CALC Problems!! Need Help Easy, QUIZ MONDAY!!?

[BeBEBanks]

Im lost on how to do these, I could really use some help on how to solve these.

1) Suppose in a right triangle, cos(t)=3/4. Find:

A) Sin(t)

B) Cot(t)

2) In a right triangle, suppose one acute angle is Pie/3 and the length of the side adjacent to that angle is 12ft. Find the length of the hypotenuse.

3) Prove the following identities.....
A) csc(t)cos(t)=cot(t)

B) sin(t)/cos(t) + cos(t)/sin(t)= 1/sin(t)cos(t)

*Please show clear steps so i can learn and understand for my precalculus test. thank you

 

[Aamir]

1. cos t = 3/4
Squaring both sides,
cos square t = 9/16
=> 1 - sin square t = 9/16
sin square t = 1 - 9/16
or sin square t = 7/16
sin t = (sqrt 7)/4
cot t = cos t/sin t
=(3/4)/(sqrt 7)/4
= 3/(sqrt 7)
2. cos (pie/3) = base/hyp
=> 0.5 = 12/hyp
=> hyp = 12/0.5 = 24 feet
3. Taking Left Hand Side,
cosec t cos t = 1/sin t * cos t
= cos t /sin t
= cot t
=Right Hand Side
Hence Proved
sin t/cos t + cos t/sin t
Taking Left Hand Side
= (sin square t + cos square t)/sin t*cos t {Taking LCM}
We know sin square t + cos square t = 1, therefore
sin t/cos t + cos t/sin t = 1/sin t*cos t
=Right Hand Side
Hence Proved

 

[ErinM1]

I've scanned my work for you so you can see. It's a lot easier than trying to type it all out. Look at it here (http://img121.imageshack.us/img121/1151/precalwork.jpg ), and I'll type some additional explanation.

1. The easiest way to find these SOHCAHTOA ratios is to draw the triangle and label the angle with all its sides. It makes them really easy to see. When you have two sides, you can just use the Pythagorean Theorem to find the last one... piece of cake! (Also, be sure to remember not to have any radicals in the denominator. If your teacher's like my teacher, your teacher will take off points, and there's no sense losing points when you did all the math correctly and found the answer.)

2. Again, when you're given a triangle, draw it. It makes life so much easier.

As for figuring out the cosine of pi/3, you can just type that into a calculator (making sure it's in radians). If you aren't allowed a calculator, well, you *could* have your unit circle memorized and know it off the top of your head, but if you're like me, a better strategy is just to figure it out with special right triangles. Remember that the formula for converting radians to degrees is times 180/pi. Degrees, at least for me, are usually easier to work with.

3. Proving trig identities is hard for a lot of people, but just remember to take the more complicated side and try to make it look like the simpler side. And memorize any identities/ratios/formulas that your teacher gave you. They'll really help you out here. If you have trouble with these, just do some practice problems (Google "trig identity practice"). They suck, but practice does make it easier.

If you have any more questions, feel free to e-mail me. Good luck!

 

[ScottV]

Assuming your working with the unit circle, then these six equations will help solve your problems:
_______________________
sin(t) = y/r -------- csc(t) = r/y

cos(t) = x/r ------- sec(t) = r/x

tan(t) = y/x ------- cot(t) = x/y
_______________________
In a right triangle, remember the Pythagorean theorem:

a^2 + b^2 = c^2, where a and b are the short and long legs, and c is the hypotenuse.

or in this case,

x^2 + y^2 = r^2
_______________________
In the unit circle, r is the radius and always equals 1 and always acts as the hypotenuse of your triangle.

r = 1

[x, y] = use the equations posted above to solve for the values of x and y.