Question

sin(2A+30°) = -1/2 how do you find the solution for that?

Answer 1

at first i thought i could use the sum difference identity but that does not seem like it would work because i do not know the value of 2A

Answer 2

look when does sin get negative

Answer 3

No need for sum difference identity

Answer 4

consider 2A+30=X solve for x
then replace that with 2A+30m how is that

Answer 5

it goes neg in q3 and q4

Answer 6

ok then fo what values does sin equal 1/2

Answer 7

so would i just get what sin of 1/2 equals as theta hat ?

Answer 8

and multiply that by whatever to get to either the 3 or 4th quad?

Answer 9

yes!

Answer 10

so 7pi/6 or 11pi/6?

Answer 11

good! that's for big X what about 2A+30

Answer 12

so it would be 210° + 360k where k represents all real numbers?

Answer 13

I think now everything is solved already ^^

Answer 14

and it would be 330° +360k where k represents all real numbers?

Answer 15

do you need the answer in degree or radians?

Answer 16

he said if it starts with degrees leave it as degrees

Answer 17

ok then leave, don't you need to solve for A?

Answer 18

because that's the answer for 2A+30

Answer 19

btw he said the answers are 90° + 180°k and 150° 180°k where k is all real numbers

Answer 20

solve for A and see what happens

Answer 21

you should get those two answer I guess

Answer 22

hmmm lemme check

Answer 23

ok

Answer 24

nope neither gives me those answers

Answer 25

hmm let me see

Answer 26

okie i pretty sure im not doing anything wrong but i am human after sorta our nature to get stuff wrong lol cant learn without making mistakes :)

Answer 27

Check again, I got those answers

Answer 28

did you solve 2A+30=210+ 360k

Answer 29

hold up i just realized something lol 2A = 90 because a =45 degrees right?

Answer 30

nope i dont think i set them equal to each other. mind if i ask why we are setting them equal to each other?

Answer 31

we started with sin(2A+30)=-1/2
then we said that 2A+30 = 210 + 360k or 2A+30= 330 +360k right?

Answer 32

we need to solve for angle A

Answer 33

oh ya alright im with you so far

Answer 34

oh so in order to do that you have to alright i think i get it

Answer 35

we just solved for 2A+30
we need to solve for A

Answer 36

Just think of 2A+30 as X in the beginning
then after replace X with 2A+3) and solve for A

Answer 37

does that make sense?

Answer 38

i think it does

Answer 39

lemme double check though

Answer 40

Ok good

Answer 41

the reason we got 210 and 330 is because sin = -1/2 in Q3 and Q4 right

Answer 42

yup, right!

Answer 43

and once we find that we just set the equation they gave us equal to Q3 and Q4 and solve correct?