Cancel Out - Maths?

Home » How To Cancel Out Cosine » Cancel Out - Maths?

Maybe your like

  • 1) Attention Class!
  • 2) Answers!
  • 3) Calendar
cancel out

When do we divide throughout by a trigo function?

Posted on April 28, 2014

From Jimmy

How do you know when you can divide throughout by a trigo function in an equation, and when you are not supposed to?

If dividing by a trigo function causes you to lose a set of solution by that trigo function, then you must factorise.

e.g:

cos x + (sin x)(cos x) = 0

If we divide by cos x, we get

1 + sin x = 0

and our answer will only come from sine function.

However, if we choose to factorise, we get

(cos x)( 1 + sin x) = 0

cos x = 0                and                1 + sin x = 0

Thus, we will have another set of solutions from the cosine function. If this is the case, DO NOT divide by a trigo function.

Here’s another case:

2 (cos x) + 3 (sin x) = 0

If we divide by cos x, we get

2 + 3 (sin x  /  cos x) = 0

2 + 3 (tan x) = 0

tan x = -2/3

Here, it looks as though we lost 2 trigo functions, sine and cosine, and ended up with only a tangent function. Thinking that we might have lost 2 sets of answers. However, since the identity states that

tan x = (sin x)/(cos x)

Both sine and cosine have already been “considered” when you find the angles that satisfy the tangent function.

In summary, unless you get a tangent (or in some cases, a cotangent) when you divide by a cosine (or in some cases, sine), DO NOT EVER DIVIDE BY A TRIGO FUNCTION!

This entry was posted in Additional Mathematics, Trigonometry, Trigonometry and tagged additional mathematics, cancel out, cos, cosine, divide, equation, factorise, sin, sine, tan, tangent, trigonometry.

Search for:

Recent Posts

  • Finding ratio of areas of non-similar shapes
  • How to find the equation of a perpendicular bisector?
  • When do we divide throughout by a trigo function?
  • 2 unknowns and 1 equation, how?
  • Differentiate ln(x+(x²+1)½) ?

Recent Comments

Archives

  • April 2014
  • March 2014

Categories

  • Additional Mathematics
  • Coordinate Geometry
  • Coordinate Geometry
  • Differentiation
  • Elementary Mathematics
  • Indices
  • logarithms
  • Quadratics
  • Similarity and Congruency
  • Trigonometry
  • Trigonometry

Meta

  • Create account
  • Log in
  • Entries feed
  • Comments feed
  • WordPress.com
Privacy & Cookies: This site uses cookies. By continuing to use this website, you agree to their use. To find out more, including how to control cookies, see here: Cookie Policy
  • Subscribe Subscribed
    • Maths?
      • Sign me up
    • Already have a WordPress.com account? Log in now.
    • Maths?
    • Subscribe Subscribed
    • Sign up
    • Log in
    • Report this content
    • View site in Reader
    • Manage subscriptions
    • Collapse this bar
Design a site like this with WordPress.comGet started

Tag » How To Cancel Out Cosine