Question

Help with four 2 part questions

Answer 1

part IA) 7pi/12 = 4pi/12 + 3pi/12, or to simplify, pi/3 + pi/4

therefore: cos(7pi/12) = cos(pi/3+pi/4)

Answer 2

for part II) use the second identity to evaluate cos(pi/3 + pi/4) using the appropriate values from the UC

Answer 3

\[\frac{ \sqrt{2}-\sqrt{6} }{ 4 }\]

Answer 4

that is what I got for 1

Answer 5

good (make sure to show the steps where you substitute pi/3 and pi/4 into the identity and simplify)

Answer 6

so this cos(7pi/12) = cos(pi/3+pi/4)

Answer 7

and then the final answer?

Answer 8

you need to show that you plugged in the alpha and beta values into the identity formula and simplification

Answer 9

Got it!

Answer 10

now for numner 2

Answer 11

for tan(17pi/12) you can break this into 11pi/12 + 6pi/12

and use the tan sum identity

Answer 12

crap i just realized 11pi/12 isn't on the unit circle

Answer 13

ok, this should do it

tan(17pi/12) = tan(14pi/12 + 3pi/12) = tan(7pi/6 + pi/4)

there we go

Answer 14

this is part 1 right so next I evaluate

Answer 15

yes, use the tan sum identity to evaluate tan(7pi/6 + pi/4)

Answer 16

2+sqrt3

Answer 17

good

Answer 18

for C)

sin(135 degrees) = sin(135 degrees+60 degrees), use the sin sum to evaluate this

Answer 19

[scroll up]

Answer 20

sin(135 degrees) = sin(135 degrees+60 degrees),
sin(135 degrees) = sin(195 degrees)

Answer 21

should be sin(195 degrees) = sin(135 degrees+60 degrees) whoops

then use the sin sum to evaluate

Answer 22

\[-\frac{ -1\sqrt{+3} }{ 2\sqrt{2} }\]

Answer 23

good (the + sign is outside the radical though, it's -1 + sqrt(3) on the numerator

Answer 24

okay now d

Answer 25

tan(15) = tan(45-30) then use the tan difference identity to evaluate

Answer 26

2-sqrt3

Answer 27

I accidentally wrote tan instead of cot so do

cot(15) = cot(45-30)

Answer 28

2+sqrt3

Answer 29

good