If sin a = - 4/5

and cos a > 0, find tan a and sec a.

tan (a) = - 4/3

sec (a) = 5/3

Step-by-step explanation:

sine is opposite over hypotenuse. so no we have a triangle with a hypotenuse of 5 and an opposite side relative to some angle a of - 4. the hypotenuse is never negative.

so draw a right triangle, mark one of the non right angles as a then the side opposite to that is - 4 and the hypotenuse is 5. use the pythagorean theorem to find the remaining angle. The result could be positive or negative, but the questions specifically tells us we want the positive version.

b^2 + - 4^2 = 5^2

b = 3

tangent is opposite over adjacent. for a we know the opposite is 3now so tan (a) = - 4/3

Now, secant is 1/cos, so lets find cos (a)

cos is adjacent over hypotenuse, and we jsut found the adjacent is 3. so cos (a) = 3/5

Now 1/cos (a) = hypotenuse over adjacent so 5/3