Alecs

While evaluating the sine of a particular angle, an absent minded student failed to notice that his calculator was not in the correct angular mode. He was very lucky to end up with the right answer. What are the two smallest possible values of x such that...

Solve, algebraically or with justification (no graphing calculator solutions allowed), the following equation: tan⁡7x-sin⁡6x=cos⁡4x-cot⁡7x

What is the value of sin⁡2x given that sin⁡x+cos⁡x+tan⁡x+cot⁡x+sec⁡x+csc⁡x=7?

You are given triangle ABC. AB=13,BC=15, and CA=14. Point D is on segment BC and CD=6. Point E is on segment BC such that CE>CD and ∠BAE=∠CAD. What is the length of BE?