The angle
θ
1
θ
1

theta, start subscript, 1, end subscript is located in Quadrant
III
IIIstart text, I, I, I, end text, and
cos
⁡
(
θ
1
)
=
−
13
30
cos(θ
1

)=−
30
13

cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 13, divided by, 30, end fraction .
What is the value of
sin
⁡
(
θ
1
)
sin(θ
1

)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?

is the correct answer.

Step-by-step explanation:

It is given that  is in third quadrant.

is always negative in 3rd quadrant and also

is always negative in 3rd quadrant.

Also, we know the following identity about  and :

Put as :

We are given that

is in 3rd quadrant so is negative.

So

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!