Trigonometric Formulas, Identities and Equation

In summary, the student is given the equation cos t = 4/5 and needs to find sin 2t. They are reminded to use the double-angle formula sin 2t = 2 sint cost and are asked if they know their trig identities to solve the problem. The student then asks for clarification and later figures out the solution on their own using the Pythagorean theorem and substitution. They are reminded to not ask for the answer but to work through the problem themselves.
  • #1
palui123
15
0

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
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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?
 
  • #4
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
 
  • #5
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. . . .
 
  • #6
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).
 

FAQ: Trigonometric Formulas, Identities and Equation

What is the difference between a trigonometric formula and an identity?

A trigonometric formula is a mathematical expression that relates two or more trigonometric functions. It can be used to solve for unknown values in a triangle or to simplify complex trigonometric expressions.
On the other hand, a trigonometric identity is an equation that is always true for all values of the variable. It is used to prove other trigonometric equations and to simplify expressions by replacing them with equivalent identities.

What are some commonly used trigonometric identities?

Some commonly used trigonometric identities include the Pythagorean identities (sin²θ + cos²θ = 1), the double angle identities (sin2θ = 2sinθcosθ), and the reciprocal identities (cscθ = 1/sinθ). Other important identities include the sum and difference identities, the half angle identities, and the co-function identities.

How can trigonometric identities be used to solve equations?

Trigonometric identities can be used to simplify equations by replacing complex expressions with simpler ones. This can help in solving for unknown values and in proving that two expressions are equal. For example, if an equation contains both sine and cosine, we can use the identity sin²θ + cos²θ = 1 to simplify the equation and solve for the unknown value.

What is the unit circle and how is it related to trigonometric formulas and identities?

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define the values of trigonometric functions for any angle in terms of the coordinates of the point where the angle intercepts the circle. This is the basis for many trigonometric formulas and identities, as they are derived from the relationships between the sides and angles of a right triangle inscribed in the unit circle.

How can trigonometric formulas and identities be applied in real life?

Trigonometric formulas and identities are used in a wide range of fields, including engineering, physics, and astronomy. They can be used to calculate distances, angles, and heights in real-world applications such as surveying, navigation, and satellite communications. They are also used in the design and analysis of structures, machines, and electronic circuits that involve periodic functions.

Similar threads

Back
Top