Further trig problems (1 Viewer)

[jad_9114]

im studying from the text book and cant seem to get the following question:

simplify sin (360 - x).tan (90 - x)

the book gives the answer as -cos x but i cant seem to get it, im sure im just making the same stupid mistake over and over again but any help would be appreciated

 

[Rorix]

sin (360-x)= -sin(x)
tan(90-x)=cot(x)
-sin(x)cot(x) = -cos(x)

 

[ngai]

yup, or expand and conquer
but u needa use tan = sin/cos, or u get tan90 haha

 

[Slidey]

sin (360 - x) is sin(270 + (90-x)) so sin270cos(90-x)+cos(270)sin(90-x) which is -sinx + 0cosx = -sinx. And tan(90-x) is cot(x).

 

[Rorix]

are we competing to find the most difficult way to do the question? i'll give it a shot...

noting that cosx = lim x-> infinity 1 - x^2/2! + x^4/4! - x^6/6! ...

 

[Slidey]

I figured I'd use the mundane approach in case jad didn't see that cos(360-x) was -sinx.

 

[Estel]

Nothing beats the power series.

 

[Slidey]

^ Not exactly mundane.

 

[BlackJack]

Correction: cosx = lim <B>n</B> -> infinity of that, where n is the number of terms on RHS used to approximate cos x.