Question 155582
Draw a picture of the triangle. Since the angle is acute, it is in the first quadrant. Since sin(theta)=4/5, you can say the side opposite theta is 4 and the hypotenuse is 5. Now you are just missing one side. You can use the Pythagorean Theorem to solve for that side, or you could recognize that this is a 3-4-5 triangle. Either way, the adjacent side (along the x-axis) is 3. Now you know each side's measure. So Cos(theta)=adjacent/hypotenuse=3/5 and tan(theta)=opp/adj=4/3. Use these to find cosecant, secant, and cotangent.