# Thread: Urgent Help Needed. Algebra 3 . Fundamental Identities.

1. ## Urgent Help Needed. Algebra 3 . Fundamental Identities.

Hello, First of all I want to thank You for taking the time out of your day to read this.

I am a senior in high school, and I'm having some trouble solving these HW problems.

I would appreciate your help. It would be better if you game me the solutions and how to get there, too. Thank you.

Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

1.- -tan x cos x

2.- cotΘ sinΘ

3.- cosΘ cscΘ

4.-
(1-cosΘ) (1+secΘ)

5.- sinΘ(cscΘ-sinΘ)

2. ## Re: Urgent Help Needed. Algebra 3 . Fundamental Identities.

Hey here is the solution to the first and second.

1. tanxcosx = (sinx/cosx)*cosx since tanx = (sinx/cosx)
= sinx simplifying (cosx/cosx = 1)

2. cotxsinx = (cosx/sinx)*sinx since cotx = (1/tanx) = (cosx/sinx)
= cosx again simplifying (sinx/sinx = 1)

3. ## Re: Urgent Help Needed. Algebra 3 . Fundamental Identities.

Originally Posted by MichaelS77
Hello, First of all I want to thank You for taking the time out of your day to read this.

I am a senior in high school, and I'm having some trouble solving these HW problems.

I would appreciate your help. It would be better if you game me the solutions and how to get there, too. Thank you.

Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

1.- -tan x cos x

2.- cotΘ sinΘ

3.- cosΘ cscΘ

4.-
(1-cosΘ) (1+secΘ)

5.- sinΘ(cscΘ-sinΘ)
Well, have you started by converting everything that's not a sine or cosine into terms of sines and cosines?

4. ## Re: Urgent Help Needed. Algebra 3 . Fundamental Identities.

no, thats why im asking for help.... im lost

5. ## Re: Urgent Help Needed. Algebra 3 . Fundamental Identities.

Originally Posted by MichaelS77
no, thats why im asking for help.... im lost
basic trig identities relating tangent, cotangent, secant and cosecant to sine and cosine are at the beginning of the link ...

(these should also be in your text, and you are expected to know them)

Table of Trigonometric Identities