Question

PRECALC QUESTIONS:
1. Find 2 common angles that sum to (17pi/12)
2. Evaluate tan(17pi/12) using the sum identity for tangent.
Please help, im very confused!!

Answer 1

We want to express `(17pi)/12` as a sum/difference of common angles. The angles usually memorized are the quadrantal angles (`0,pi/2,pi,(3pi)/2,2pi,` etc...) and the multiples of `pi/6,pi/4,pi/3` .

There are an infinite number of possible answers.

Since the denominator is 12 we might select a sum/difference of angles with denominators 3 and 4. Then `(17pi)/12=(Api)/3+(Bpi)/4` .

Adding the fractions on the right hand side together we get `(4Api+3Bpi)/12` . Then setting the numerators equal we get `4A+3B=17` which again has an infinite number of solutions. One solution is to let A=2 and B=3.

Thus `(17pi)/12=(2pi)/3+(3pi)/4`

Answer 2

I realized lol...

Answer 3

you could also use
\[\frac{17\pi}{12} = \frac{5\pi}{4}+\frac{\pi}{6}\]

Answer 4

okay thanks! how do i do the second part?

Answer 5

\[\tan(a+b) = \frac{\tan a + \tan b}{1-\tan a \tan b}\]

Answer 6

how do i know what values a and b are?

Answer 7

17pi is a and 12 is b

Answer 8

So exactly how the original problem reads

Answer 9

so its
tan(17pi + 12) = tan(17pi) + tan(12) / 1-tan(17pi)tan(12) ?

Answer 10

??

Answer 11

\[\tan(\frac{17\pi}{12}) = \tan(\frac{2\pi}{3}+\frac{3\pi}{4}) = \tan(\frac{\pi}{6}+\frac{5\pi}{4})\]

Answer 12

??
looks like you need to review your basic trig
you are asked to evaluate tan(17pi/12) without calculator
the only way to do this is use common angles for which tangent ratios are known
use the formula above for angle addition to obtain exact answer for tan(17pi/12)

notice you have 2 possible combinations of common angles to use...either way you will get same answer

Answer 13

i know that you need to add the 2 angles which i did to get 255 degrees (and then of course take the tangent of that) but what i don't understand is how the sum identity has anything to do with solving it.

Answer 14

well 17pi/12 = 255 ....so adding the angles to get 255 is unnecessary

the question is how do you intend to find tan(255) without calculator?

....hence the sum identity is needed:)

Answer 15

okay thank you for all your help :)

Answer 16

yw

Answer 17

here is solution for you to check your work
http://www.wolframalpha.com/input/?i=tan%2817pi%2F12%29

Answer 18

cool thanks again!