Question

2 part question

Answer 1

for part I you can decompose 7pi/12 into 4pi/12 + 3pi/12 which are both on the unit circle

then for part II you can use the tan sum identity (last row) to find tan(7pi/12)

Answer 2

tan (a+b)=tan a + tan b / 1-tan a tan b

Answer 3

yes but you have to plug in 4pi/12 and 3pi/12 for alpha and beta

Answer 4

also be careful with parentheses

tan (a+b)= (tan a + tan b) / (1-tan(a) *tan (b))

Answer 5

tan ( 4pi/12 +3pi/12)=(tan 4pi/12 + tan 3pi/12) / 1-tan (4pi/12) * tan (3pi/12))

Answer 6

good


then you just plug in the appropriate values from the UC

Answer 7

tan(4pi/12) = ?
tan(3pi/12) = ?

Answer 8

note that 4pi/12 = pi/3 and 3pi/12 = pi/4

both tan(pi/3) and tan(pi/4) can be calculated using the fact that tan(x) = sin(x)/cos(x)

Answer 9

sqrt2/2 , sqrt2/2

Answer 10

okay so part I is 4pi/12 + 3pi/12
part II : tan ( 4pi/12 +3pi/12)=(tan 4pi/12 + tan 3pi/12) / 1-tan (4pi/12) * tan (3pi/12))

sqrt2/2 , sqrt2/2

Answer 11

tan(4pi/12) and tan(3pi/12) only have one solution each, you should not be getting a coordinate (x,y)

Answer 12

for tan(3pi/12), sin(3pi/12) = sqrt(2)/2 and cos(3pi/12) = sqrt(2)/2 right? then what does tan(3pi/12) equal?

Answer 13

sqrt(2)/2

Answer 14

remember that tan(x) = sin(x)/cos(x)

Answer 15

sin(3pi/12) = sqrt(2)/2
cos(3pi/12) = sqrt(2)/2

tan(3pi/12) = sin/cos = ?

Answer 16

so we know that sin and cos are both sqrt(2)/2 right?

[ sqrt(2)/2 ] / [sqrt(2)/2] = ?

Answer 17

=1

Answer 18

good

so tan(3pi/12) = 1

repeat this same logic with tan(4pi/12)

Answer 19

what are the sin and cos values of tan(4pi/12)?

Answer 20

remember that 4pi/12 is the same as pi/3

look at the UC to find the sin and cos values for pi/3

Answer 21

1/2 , sqrt3,2

Answer 22

good

so tan(4pi/12) = ?

Answer 23

sqrt3

Answer 24

good

so tan(3pi/12) = 1 and tan(4pi/12) = sqrt(3)

now plug these values into

(tan 4pi/12 + tan 3pi/12) / 1-tan (4pi/12) * tan (3pi/12))

Answer 25

(sqrt3+ 1) / 1-sqrt3 * 1))

Answer 26

good

since we generally don't want radicals in the denominator

you can multiply the numerator and denominator by the conjugate of the denominator

in other words, multiply the numerator and the denominator by (1+sqrt(3))

then use foil to simplify

Answer 27

1/1+sqrt3

Answer 28

use FOIL on both the numerator and denominator to simplify the expression

Answer 29

-2-sqrt3

Answer 30

good that's your sol'n

Answer 31

gtg