Answer:
[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]
Step-by-step explanation:
The complete question is
The angle θ1 is located in Quadrant 1, and cos (θ1)=10/17.
What is the value of sin(θ1)?
we know that
[tex]sin^2(\theta_1)+cos^2(\theta_1)=1[/tex] ---> trigonometric identity
we have
[tex]cos(\theta_1)=\frac{10}{17}[/tex]
The angle [tex]\theta_1[/tex] is located in Quadrant I, that means the sine of angle [tex]\theta_1[/tex] is positive
substitute the given value in the trigonometric identity
[tex]sin^2(\theta_1)+(\frac{10}{17})^2=1[/tex]
[tex]sin^2(\theta_1)+\frac{100}{289}=1[/tex]
[tex]sin^2(\theta_1)=1-\frac{100}{289}[/tex]
[tex]sin^2(\theta_1)=\frac{189}{289}[/tex]
take square root both sides
[tex]sin(\theta_1)=\pm\frac{\sqrt{189}}{17}[/tex]
Remember that the sine is positive (Quadrant I)
so
[tex]sin(\theta_1)=\frac{\sqrt{189}}{17}[/tex]
Simplify
[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]
