Acute angle W has sin W = 1/2 and sec W=2/sqrt 3. Which are values of csc W and cos W?
To find the values of csc W and cos W, we can use the Pythagorean identity for the trigonometric functions.
Given that sin W = 1/2, we know that the opposite side is 1 and the hypotenuse is 2. Using the Pythagorean theorem, we can find the adjacent side to be √3.
So, we have sin W = 1/2, cos W = √3/2, and sec W = 2/√3.
From sec W = 1/cos W, we can find that cos W = 1/sec W = 1/(2/√3) = √3/2.
Finally, we can find the value of csc W using the Pythagorean identity:
csc^2 W = 1 + cot^2 W
csc^2 W = 1 + (cos^2 W / sin^2 W)
csc^2 W = 1 + ((√3/2)^2 / (1/2)^2)
csc^2 W = 1 + (3/4) / (1/4)
csc^2 W = 1 + 3
csc^2 W = 4
csc W = 2
Therefore, the values of csc W and cos W are csc W = 2 and cos W = √3/2.