Question

Find the exact value of each expression:
a. sin20degcos80de-cos20degsin80deg

b. cos 5pi/12cos7pi/12-sin5pi/12sin7pi/12

Answer 1

@jim_thompson5910 does that make sense or should i write out again?

Answer 2

you don't need to write "deg"

Answer 3

hint:

see page 2 of http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf specifically the "Sum and Difference Formulas" section

Answer 4

so it would be the formula stating that sin(a +or-b)=sinacosb-cosasinb?

Answer 5

correct

Answer 6

you'll use the cosine version for part b

Answer 7

oh okay so for the test tomorrow I should just memorize those formulas?
but so now to solve it, it would be
(20+80) or (20-80)?
so the answer is 100 or -60?

Answer 8

sin(20)cos(80)-cos(20)sin(80) = sin(20-80) = sin(-60) = ???

Answer 9

oh wait oops

Answer 10

would it be sin(60)?

Answer 11

@jim_thompson5910

Answer 12

sin(-60) is not equal to sin(60)

Answer 13

oh .. i thought you put the question marks as in that it was wrong

Answer 14

no it's my way of putting a blank

Answer 15

it's pi/3

Answer 16

so you'd fill in the blank

Answer 17

ohh ok sorry

Answer 18

sin(-60) = -sin(60) = _______________

Answer 19

-pi/3

Answer 20

@jim_thompson5910

Answer 21

no not -pi/3

Answer 22

you're thinking of -60 degrees = -pi/3 radians

Answer 23

use the unit circle and determine -sin(60)

Answer 24

okay i've been looking at the unit circle for 5 minutes and because you're determining -sin60 you would be looking in the 3 and fourth quadrants right?

Answer 25

and looking for a distance of 60 degrees the opposite way? I'm just trying to remember what my teacher said.. He said something like that @jim_thompson5910

Answer 26

determine the y coordinate of that point, then make it negative

that will be the value of -sin(60)

Answer 27

root 3/2?

Answer 28

\[\Large \sin(60) = \frac{\sqrt{3}}{2}\]

\[\Large -\sin(60) = -\frac{\sqrt{3}}{2}\]

Answer 29

okay so I just look for it on the unit circle and determine it through the coordinate?

Answer 30

yes, x = cos(theta) and y = sin(theta)

Answer 31

ok! got it!

Answer 32

now for part b do you find pi/6 on the unit circle and look at x coordinate to determine the value?

Answer 33

@jim_thompson5910