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