Trigonometry Answers

Mr Mcbean is a very keen fisherman who will go fishing at any time of the day or night. He requires 1.5 metres of water at the boat ramp (i.e. 1.5 above the mean sea level) to launch his boat the "periodic function". The next high tide occurs at 2 am at a height of 2.8m above the mean sea level.
Find the times in the first 24 hours after 2am when he is able to launch his boat.

Find an expression for the trigonometric equation:
F= 6 sin 8πt - 8 cos 8πt in the form : R sin (ωt+ α) and investigate its waveform over one cycle.

Frank and Marie set sail from the same point. Frank is sailing in the direction S7∘E. Marie is sailing in the direction S13∘W. After 5 hours, Marie was 16 miles due west of Frank. How far had Marie sailed?
Round your answer to four decimal places.

(1) Solve sin x cos x = 0.

(2) Solve 2 sin2 x − sin x − 1 = 0.

(3) Solve cos x + cos 2x = 0.

(4) Solve 2 cos x + sec x = 3.

(5) Solve sec x − 1 = tan x.

Directions: show the steps that leads to the answers

For each problem, determine the values of x such that 0 ≤ x < 2π that satisfy equation.

(1) Solve sin x cos x = 0. (Answers: x = 0, π/2, π, 3π/2)

(2) Solve 2 sin2 x − sin x − 1 = 0. (Answers: x = π/2, 7π/6, 11π/6)

(3) Solve cos x + cos 2x = 0. (Answers: x =π/3, π, 5π/3)

(4) Solve 2 cos x + sec x = 3. (Answers: x = 0, π/3, 5π/3)

(5) Solve sec x − 1 = tan x. (Answer: x = 0)

(1) Evaluate exactly tan (Arccos 2/3)

(2) Evaluate exactly cos (Arcsin 1 + Arccos 1/2)

(3) Determine arcsin 1/√2
Careful: that is arcsin and not Arcsin, so there are going to
be infinitely many answers. You need to give all of them.

(4) Evaluate exactly sin( 1/2 Arcsin 4/5)

(5) Use a calculator to determine Arctan 10 in radians to two decimal places.

(1) Using an identity from this section, write sin 7x − sin 3x as a product.
(2) Using an identity from this section, find the exact value of sin 105◦
sin 15◦
(3) Using an identity from this section, find the exact value of sin 195◦
cos 75◦
(4) Using identities from this section, verify the identity cos t−cos 3t over sin t+sin 3t = tan t.
(5) Using an identity from this section, write sin 7x sin 3x as a sum or a difference.

Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

cos3x
Question options:

cos x - cos 3x

cos x + cos 3x

cos x - cos 3x - cos 2x

cos x + cos 3x + cos 2x

Given tan(A) = (3/4), 0 < A < (π/2) and cos(B) = (5/13), (3π/2) < B < 2π) determine cos(2A)

Given tan(A) = (3/4), 0 < A < (π/2) and cos(B) = (5/13), (3π/2) < B < 2π) determine sin(A - B)