Question

Degrees or Radians for this? What should the answer roughly look like?

Answer 1

I know how to get the hypotenuse. How do I answer the rest?

Answer 2

and do I use degrees or radians for my calculations?

Answer 3

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).

Answer 4

thanks but i said i already know that, i'm asking about the functions

Answer 5

Ok. Lets take a look. I believe they want cos, sin, tan, sec, csc and cot of angle theta is that right?

Answer 6

yep

Answer 7

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?

Answer 8

yeah i got 15

Answer 9

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.

Answer 10

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

Answer 11

Tan(theta) = sin/cos = 0.8/0.6 = 4/3.

Answer 12

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

Answer 13

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?

Answer 14

Yes.

Answer 15

right exactly
you can find the angles using the inverse trig buttons on your calculator, but they are not necessary for the problem

Answer 16

again i say it is a bit odd, because you are asked to find
\[f(a)\] without knowing "a"

Answer 17

so, last question: what is the difference between radians and degrees?

Answer 18

2*pi*rad = 360 degrees is your conversion.

Answer 19

So if you take 360 and divide by 2*pi this will give you the number of radians in 360 or approx 57.297

Answer 20

If you are using your calculator the compute the angles you must be sure which mode your calculator is in, either radians or degrees.

Answer 21

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).