The angle \theta_1θ
1

theta, start subscript, 1, end subscript is located in Quadrant \text{III}IIIstart text, I, I, I, end text, and \cos(\theta_1)=-\dfrac{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(\theta_1)sin(θ
1

)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.

The value will be  .

Given,

.

And lies in the third quadrant.

We know that,

Since,  

Here, and .

Now, applying Pythagoras theorem, we get

Hence,

Since lies in the third quadrant, so

Hence, the value of is .

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sin ( θ ) = 3√21 / 17

Step-by-step explanation:

Given:-

- The angle (θ) lies in the first quadrant. Where theta is defined as:

                              cos ( θ ) = 10 / 17

Find:-

- Find sin ( θ ) :

Solution:-

- We will draw a right angle triangle in the first quadrant. With base, B = 10 and hypotenuse H = 17. Since,

                              cos ( θ ) = B / H = 10 / 17

- Using pythagorean theorem determine the perpendicular side length:

                              H^2 - B^2 = P^2

                              17^2 - 10^2 = P^2

                              √189 = P

                             P = 3√21

- Now evaluate sin ( θ ):

                              sin ( θ ) = P / H

                              sin ( θ ) = 3√21 / 17

6 cm

step-by-step explanation: