How Can I Simplify Trigonometric Expressions in My Homework?

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SUMMARY

The discussion focuses on simplifying the trigonometric expression tan(x) cos(x). The user initially transforms the expression into sin(x) / cos(x) cos(x) but struggles to proceed further. A participant advises that by recognizing sin(x) / cos(x) equals tan(x) and simplifying the expression, the result is simply sin(x). The conversation emphasizes the importance of foundational algebra skills in tackling trigonometric simplifications.

PREREQUISITES
  • Understanding of basic trigonometric identities, specifically tan(x) = sin(x) / cos(x)
  • Familiarity with algebraic manipulation, including multiplication and division of fractions
  • Knowledge of the properties of sine and cosine functions
  • Ability to recognize and apply restrictions in mathematical expressions
NEXT STEPS
  • Study trigonometric identities and their derivations, focusing on sine, cosine, and tangent functions
  • Practice algebraic simplification techniques, particularly with trigonometric expressions
  • Learn about the concept of restrictions in rational expressions and their implications
  • Explore advanced trigonometric functions and their applications in calculus
USEFUL FOR

Students learning trigonometry, educators teaching trigonometric simplifications, and anyone seeking to strengthen their algebraic manipulation skills in relation to trigonometric functions.

Arsonade
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i have some problems (37 actually) that i have tried vvery much to work on and have gotten nowhere

just to give you an example, the first one is

tanx cosx i have to simplify this

the first thing i would do is make it

sinx
cos cosx but after this I am stumped. the other problems are along this same idea

i do not think that i will get much acomplished doing this on a fourum so if anyone would be so kind as to help me, my AIM sn is AdamChess4.

thank you and i would really apriciate any help you can give me.

Adam
 
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simplify

tan(x)cos(x) ?

\frac{sin(x)}{cos(x)}cos(x).. you can't seriously not know what to do next..
 
well, i honestly dont, e are just learning this and i am having trouble finding LCDs and factoring these types of operations,
Adam
 
Arsonade said:
well, i honestly dont, e are just learning this and i am having trouble finding LCDs and factoring these types of operations,
Adam


Ok. In that expression you have sin x/cos x, so you're dividing by cosine. Then you multiply by cosine. What happens?
 
i'd suggest you brush up on a little algebra before tackling any trig
 
I can only imagine you are getting intimidated by the sin(x) and cos(x) functions. Try writing y = sin(x) and x = cos(x) then simplify. Hopefully going through this exercise will be helpful.
 
\frac{sinx}{cosx}=tanx

\frac{sinx}{cosx} \times cosx

The two cosx gets crossed out.

then you get sinx

Maybe I am wrong.
 
Last edited:
when

x
-- y
y

= x
there's a restriction that y cannot be 0 though, but in most cases its irrelevant

when

x
---
y/x

you change this to multiplication
x * x/y

x^2/y

Hope this helps!
 

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