Answer:
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
The value will be [tex]sin\theta_{1} =-\dfrac{\sqrt{731} }{\rm 30}[/tex].
Given,
[tex]\rm cos\rm \theta_{1} =-\dfrac{13}{30}[/tex].
And [tex]\theta_{1}[/tex] lies in the third quadrant.
We know that,
[tex]\rm cos\theta=\dfrac{\rm base}{\rm hypotenuse}[/tex]
Since, [tex]\rm cos\rm \theta_{1} =-\dfrac{13}{30}[/tex]
Here, [tex]\rm base=13[/tex] and [tex]\rm hypotenuse=30[/tex].
Now, applying Pythagoras theorem, we get
[tex]\rm hypotenuse^{2} =\rm perpendicular^{2} +\rm Base^{2}[/tex]
[tex]30^{2} =\rm perpendicular^{2} +13^{2}[/tex]
[tex]900 =\rm perpendicular^{2} +169[/tex]
[tex]731 =\rm perpendicular^{2}[/tex]
[tex]\rm perpendicular=\sqrt{731}[/tex]
Hence,
[tex]sin\theta_{1} =\dfrac{\rm perpendicular}{\rm hypotenuse}[/tex]
[tex]sin\theta_{1} =\dfrac{\sqrt{731} }{\rm 30}[/tex]
Since [tex]\theta_{1}[/tex] lies in the third quadrant, so
[tex]sin\theta_{1} =-\dfrac{\sqrt{731} }{\rm 30}[/tex]
Hence, the value of [tex]sin\theta_{1}[/tex] is [tex]-\dfrac{\sqrt{731} }{\rm 30}[/tex] .
For more details on trigonometric ratio follow the link:
https://brainly.com/question/1201366
