Use Identities to find the value of each expression.

Question

Find Cos theta and sec theta if tan theta equals -2 and sin theta is greater than zero.

Answer 1

tan(theta) = -2 = opposite side over adjacent side= 2/-1 is sin(theta) > 0, theta is in quadrant II where the adjacent side < 0 and cos(theta) < 0

hypotenuse squared = sum of squares of the other two sides = (2)^2 + (-1)^2 = 5

hypotenuse= sqr5

cos(theta) = adjacent side over hypotenuse = -1/sqr5

sec(theta) = 1/cos(theta) = -sqr5