Trigonometric Formulas, Identities and Equation

AI Thread Summary
To find sin 2t when cos t = 4/5, first determine sin t using the Pythagorean theorem, resulting in sin t = 3/5. The double-angle formula sin 2t = 2 sin t cos t can then be applied. Substituting the known values gives sin 2t = 2(3/5)(4/5), simplifying to sin 2t = 24/25. The discussion highlights the importance of understanding trigonometric identities and the need for collaborative problem-solving.
palui123
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Homework Statement


t = tetha

FInd sin 2t when cos t = 4/5

Homework Equations



no idea

The Attempt at a Solution



no. . . . btw what should I do 1st? I don't understand this question
 
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1) You are given that cos t = 4/5. Can you find sin t?
2) Do you know your trig identities? Particularly the double-angle formulas.
 
palui123 said:

Homework Statement


t = tetha

FInd sin 2t when cos t = 4/5

Homework Equations



no idea

The Attempt at a Solution



no. . . . btw what should I do 1st? I don't understand this question
Exactly what part of "Find sin 2t" do you not understand?
 
Formula:
Sin2t = 2 sint costWhat I do is:
Sin2t = 2sint cost

since cost = 4/5

sin2t = 2sint (4/5)

sin2t = 8sint/5

What should I do then..? I know its wrong
 
w8. . . nvm. I know how to this question now.

sin 2t = 2 sint cost

since cost = 4/5 ,

a=4 , h=5 , o=??

P.theorem:
a^2=b^2+c^2
o=3

then sint = 3/5

then subtitude =D . . . solve get the answer. . .I'm talking by myself T-T ask = me , answer = me T-T . AID ME NEXT TIME PLEASE. . . .
 
palui123 said:
I'm talking by myself T-T ask = me , answer = me T-T . AID ME NEXT TIME PLEASE. . . .
If by "aiding you" you mean, show you the work + answer, then NO, WE CAN'T DO THAT. Read the forum rules. Otherwise, I think I gave you sufficient aid in my post (#2).
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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