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Use the exponential definition of sinh(x) and cosh(x) to show cosh (X) = cosh(2x)+2 b) Solve the equation 6 cosh(4x) + 30 sinh(4x) = 15, giving your answer in terms of a natural logarithm
Question 2 (4 marks total)
Without using a calculator, solve the following system of equations for x E and y E , given: a) log2(m2 — 6m) = 2 log2(1 — m) — 2 (1 marks) b) 24Y+1 — 3Y = 0 (1 marks)
c) 4Y I=32 log3(x— y)+ log3(x+ y) = I
(2 marks)
Hint: Solving these problems will require careful application of exponent and logarithm identities. Question 3 (3 marks total) Prove the following identities a) tan( x + 1i) = — cot x b) cos (x—y) = tan x + cot y cos x cos y C) cosx(1—cos(2.0) = sin xsin (2x)
Hint: Do not attempt to substitute values and then solve. You must arrive at a solution algebraically through application of trigonometric identities.
Question 4 (4 marks total)
Solve the following trigonometric equations, for 0

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The Communications Loop (see diagram) is a critical part of every single flight. It is virtually impossible to engage in any flight activity, from general aviation to military tactical flying, without the use of some degree of communication. This communication might be between the pilot and other crew members, ATC, dispatch, Flight Service, or even other aircraft. Methods of communication might include verbal, body language (such as hand gestures), written, or data link/CPDLC. However, despite how critical communication is, research has shown that pilots and controllers make MANY communication errors. Why is this? For this discussion, you will consider common causes for breakdowns in the Communication Loop. Determine the meaning of “Noise” and “Filters” in the Communication Loop diagram. List at least five (5) common filters or barriers to communication. You may use examples from your own experiences. Then recommend methods to overcome filters in communication. Is one of the listed methods of communication less susceptible to noise, filters, and errors? If so, which one, and why?

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