Answer :
Given: sin R = 0.35
We know that sin R = opposite/hypotenuse in a right triangle.
Let’s assume the opposite side is x and the hypotenuse is y.
So, sin R = x/y
Given sin R = 0.35, we have:
0.35 = x/y
To find cos R, we can use the Pythagorean identity: sin^2 R + cos^2 R = 1
Substitute sin R = 0.35 into the equation:
(0.35)^2 + cos^2 R = 1 0.1225 + cos^2 R = 1 cos^2 R = 1 - 0.1225 cos^2 R = 0.8775
Taking the square root of both sides to solve for cos R:
cos R = √0.8775 cos R ≈ 0.94
Therefore, the value of cos R rounded to the nearest hundredth is approximately 0.94.
We know that sin R = opposite/hypotenuse in a right triangle.
Let’s assume the opposite side is x and the hypotenuse is y.
So, sin R = x/y
Given sin R = 0.35, we have:
0.35 = x/y
To find cos R, we can use the Pythagorean identity: sin^2 R + cos^2 R = 1
Substitute sin R = 0.35 into the equation:
(0.35)^2 + cos^2 R = 1 0.1225 + cos^2 R = 1 cos^2 R = 1 - 0.1225 cos^2 R = 0.8775
Taking the square root of both sides to solve for cos R:
cos R = √0.8775 cos R ≈ 0.94
Therefore, the value of cos R rounded to the nearest hundredth is approximately 0.94.
Answer:
[tex]\sf \cos R = \boxed{0.94} [/tex]
Step-by-step explanation:
To find the cosine of angle [tex]\sf R [/tex] in the right triangle when the sine of angle [tex]\sf R [/tex] is given, we can use the Pythagorean identity [tex]\sf \sin^2 R + \cos^2 R = 1 [/tex].
Here's how to do it:
Given:
[tex]\sf \sin R = 0.35 [/tex]
Use the Pythagorean identity:
[tex]\sf \sin^2 R + \cos^2 R = 1 [/tex]
Substitute the value of [tex]\sf \sin R [/tex]:
[tex]\sf (0.35)^2 + \cos^2 R = 1 [/tex]
Solve for [tex]\sf \cos^2 R [/tex]:
[tex]\sf \cos^2 R = 1 - (0.35)^2 [/tex]
[tex]\sf \cos^2 R = 1 - 0.1225 [/tex]
[tex]\sf \cos^2 R = 0.8775 [/tex]
Take the square root of both sides to find [tex]\sf \cos R [/tex]:
[tex]\sf \cos R = \sqrt{0.8775} [/tex]
[tex]\sf \cos R = 0.9367496997597[/tex]
[tex]\sf \cos R = 0.94 \textsf{(Rounding to the nearest hundredth)} [/tex]
Therefore, [tex]\sf \cos R = \boxed{0.94} [/tex].