There are three problems posted.

Section on using the properties of algebraic, trigonometric, logarithmic and exponential functions to solve problems. 1) Solve the following equation: log5 X + log5(X-2) = log5 X 2) The half-life of a certain radioactive element is 100days. That means that after 100 days ½ of the radioactive substance will have decayed to one half of its original amount. How long will it take to decay to ¼ of the original amount if decay equation is of the form A(t) = Ce^kt where C is the amount of substance. 3) Show on unit circle: sin(- x) = -sin x, cos(- x) = cos x, and what tan(- x) equals.

Two problems posted.

1) Prove from the unit circle that sin²⊖ + cos²⊖ = 1. Using the result describe the equation for which x = 3 + 2cos⊖, y = 1 + 3sin⊖. 2) Using problem one simplify sin²⊖/(1 + cos⊖) + sin²⊖/(1 - cos⊖)

fundamental identities

Use the fundamental identities to find the value of the trigonometric function. Find csc s if sin s = - 2/3 and s is in quadrant IV. Which one is the correct answer. -√7/9 5/4 3√7/7 - 3/2

Trigonometric Identities; Exact Value

Use trigonometric identities to find the exact value of the attached equation. Which of the attached answers is correct?

Identity

Find the exact value by using a sum or difference identity. Which is the correct answer? cos 20 cos 25 - sin 20 sin 25 (angles are in degrees) 1 -√2/2 √2/2 √3/2