Questions like this are going to be on my next exam and I have no idea how to do this..

Question

Classify f(θ) of these trigonometric functions as less than, greater than, or equal to zero. 

 

A. f(θ)=sinθ, θ is in quadrant III

B. f(θ)=tanθ, θ is in quadrant II

C. f(θ)=cosθ, θ in quadrant IV

D. f(θ)=cosθ, θ=180 degrees

E. f(θ)=tanθ, θ= 540 degrees 

F. f(θ)=tanθ,θ is in quadrant I

Answer 1

If you want to learn easy ways to remember all your trig,

Google "Trig Without Tears"  by Stan Brown

 

Sorry, I can't explain the easiest way to Understand and Remember the signs

      of trig functions on here because I can't draw pictures;

      BUT there is a mnemonic to help you in a crunch.

I don't like mnemonics because they don't help you understand it;

      but they can help in a pinch.

 

It is   All  Students  Take  Calculus.

For quadrants 1, 2, 3, 4

In 1 - all are positive.

In 2 - only the Sine is positive.

In 3 - only the Tangent is positive.

In 4 - only the Cosine is positive.

BUT Unfortunately this doesn't really help for angles

  on the X and Y axises.  e.g. - 0, 90, 180, 270, 360 degrees.

 

I hope you remember which quadrant is which :)

 

1 - is 0 to 90 degrees

2 - is 90 to 180 degrees

3 - is 180 to 270 degrees

4 - is 270 to 360 degrees

 

Going Counter Clockwise from the (+) X axis

like this:

           |

      2   |   1

--------|--------

      3   |   4

           |

 

Answer 2

In quadrant I, all trig function values are positive.

 

In quadrant II, sine and its reciprocal (cosecant) are positive, the others are negative.

 

In quadrant III, tangent and its reciprocal (cotangent) are positive, the others are negative.

 

In quadrant IV, cosine and its reciprocal (secant) are positive, the others are negative.