The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{10}{17}cos(θ 1 )= 17 10 cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 10, divided by, 17, end fraction . What is the value of \sin(\theta_1)sin(θ 1 )sin

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