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and do I use degrees or radians for my calculations?
In order to computer the hypotenuse you do not need radians or degrees. To find the hypotenuse or more appropriately the length of the hypotenuse use Pythagorean theorem. Which is length of hypotenuse = sqrt( a^2 + b^2).
thanks but i said i already know that, i'm asking about the functions
Ok. Lets take a look. I believe they want cos, sin, tan, sec, csc and cot of angle theta is that right?
Ok. First we need to compute the length of the hypotenuse. For #1 that would be sqrt(144 + 81) = 15. Is that what you get?
yeah i got 15
Ok. The cos of theta is the length of the side opposite the angle theta divided by the length the hypotenuse. or cos(theta) = 9/15 = 3/5 = 0.6. For sin(theta) = length of adjacent side from theta/ hypotenuse = 12/15 = 4/5 = 0.8.
the thing about these problems that are confusing (and math teachers never mention is) is that you are asked to evaluate a function at a number, but you do not know what that number is. in fact it is not important because you are really being asked for ratios of sides of a triangle
Tan(theta) = sin/cos = 0.8/0.6 = 4/3.
commdoc has your answers, and in truth it doesn't matter how you measure the angle because if you measure it in radians then you would take your sine and cosine etc as functions of radians, and if you measured in degrees you would take them in degrees
okay i understand...so you only need to know how to functions work in respect to the sides of the triangle? you do not need to know the angle values for this problem?
right exactly you can find the angles using the inverse trig buttons on your calculator, but they are not necessary for the problem
again i say it is a bit odd, because you are asked to find \[f(a)\] without knowing "a"
so, last question: what is the difference between radians and degrees?
2*pi*rad = 360 degrees is your conversion.
So if you take 360 and divide by 2*pi this will give you the number of radians in 360 or approx 57.297
If you are using your calculator the compute the angles you must be sure which mode your calculator is in, either radians or degrees.
Satellite is right about calculating the function. Here we are calculating the inverse problem where f(a) = x. We know x but we want to know a. Here a = f^-1(x).