The angle \theta_1θ 1

theta, start subscript, 1, end subscript is located in Quadrant \text{II}IIstart text, I, I, end text, and \cos(\theta_1)=-\dfrac{12}{19}cos(θ
1

)=−
19
12

cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 12, divided by, 19, end fraction .
What is the value of \sin(\theta_1)sin(θ
1

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

Step-by-step explanation:

It is given that:

And we have to find the value of

As per trigonometric identities, the relation between can represented as:

Putting in place of Because we are given

Putting value of cosine:

It is given that is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option