Trig word problems

[killasnake]

I have 3 questions the first one is. Writing the correct "wording" of the problem

Suppose you wish to express sin(3t) in terms of sint and cost. Apply the sum formula to sin(3t)= sin(t+2t) to obtain an expression that contains sin(2t)= sin(t+t) and cos(2t)= cos(t+t). Apply the sum formulas to those two expressions. Enter the resulting expression for sin(3t) here
_____________________,
using S to denote sint and C to denote cost. For example, if your answer was 3sintcost you'd simply enter 3*S*C.

"Sooo huh?"

and

We did this problem in class. This is just to refresh your memory, so that you can solve the next problem. A ship is moving due west at 8 knots. You are in a speed boat [sqrt]2 nautical miles directly southeast of the ship. (Thus your bearing as seen from the ship is 135 degrees.) You need to catch up with the ship, and you can move at a speed of 16 knots. So you take off at a bearing of ____________ degrees, and you reach the ship in ____________ minutes. Enter your answers as decimal expression with at least four digits, or enter mathematical expressions.

and

This is like the preceding problem, except that the numbers are a little different. A ship is moving due west at 10 knots. You are in a speed boat at a distance of 4 nautical miles from the ship. Your bearing as seen from the ship is 142 degrees. You need to catch up with the ship. So you take off at a speed of 15 knots and a bearing of ________________ degrees, and you reach the ship in _____________ minutes. Enter your answers as decimal expression with at least four digits, or enter mathematical expressions.

How do I start the two word problems?

 

[stapel]

1) This is long and may be messy, but you only need to follow the instructions to (eventually) get what they're looking for. How far have you gotten?

2 & 3) What do you have in your notes from the problem done in class? Where are you stuck in re-working (2) and doing (3)?

Eliz.

 

[soroban]

Hello, killasnake!

Suppose you wish to express \(\displaystyle \sin(3t)\) in terms of \(\displaystyle \sin(t)\) and \(\displaystyle \cos(t).\)
Apply the sum formula to \(\displaystyle \sin(3t)\,=\,\ sin(t+2t)\) to obtain an expression
that contains \(\displaystyle \sin(2t)\,=\,\sin(t+t)\) and \(\displaystyle \cos(2t)\,=\,\cos(t+t).\)
Apply the sum formulas to those two expressions.

The directions are not well-stated . . . causing more confusion than enlightenment.

We are expected to know these two "sum formulas":
. . . \(\displaystyle \sin(A\,\pm\,B)\:=\:\sin(A)\cdot\cos(B)\quad\pm\,\sin(B)\cdot\cos(A)\)
. . . \(\displaystyle \cos(A\,\pm\,B)\:=\:\cos(A)\cdot\cos(B)\,\mp\,\sin(A)\cdot\sin(B)\)

and their special cases:
. . . \(\displaystyle \sin(2A)\:=\:2\cdot\sin(A)\cdot\cos(A)\)
. . .\(\displaystyle \cos(2a)\:=\:\cos^2(A)\,-\,\sin^2(A)\)


We have: .\(\displaystyle \sin(3t)\;=\;\sin(2t\,+\,t)\)

. . . . . \(\displaystyle =\;\;\;\;\;\underbrace{\sin(2t)}\cdot\cos(t)\;\;\;\;\;+\;\;\;\;\;\sin(t)\cdot\underbrace{\cos(2t)}\)

. . . . . \(\displaystyle =\:[\overbrace{2\cdot\sin(t)\cdot\cos(t)}]\cdot\cos(t)\,+\,\sin(t)\cdot[\overbrace{\cos^2(t)\,-\,\sin^2(t)}]\)

. . . . . \(\displaystyle =\;2\cdot\sin(t)\cdot\cos^2(t)\,+\,\sin(t)\cdot\cos^2(t)\,-\,\sin^3(t)\)

. . . . . \(\displaystyle =\;3\cdot\sin(t)\cdot\cos^2(t)\,-\,\sin^3(t)\)