If sin theta equals two third and zero degrees less than theta less than 90 degrees find cosine theta
To find the value of cosine(theta) given that sin(theta) = 2/3 and 0 degrees < theta < 90 degrees, we can use the Pythagorean identity:
sin^2(theta) + cos^2(theta) = 1
First, we can find the value of cos^2(theta) by substituting sin(theta) into the equation:
(2/3)^2 + cos^2(theta) = 1
4/9 + cos^2(theta) = 1
cos^2(theta) = 1 - 4/9
cos^2(theta) = 5/9
Taking the square root of both sides, we get:
cos(theta) = sqrt(5/9)
Since 0 degrees < theta < 90 degrees, we know that cosine(theta) is positive. Therefore,
cos(theta) = sqrt(5/9) = sqrt(5)/3
So, the value of cosine(theta) is sqrt(5)/3.