Which is positive when 90° < x < 180°?

[fork]

If 90 degree < x < 180 degree, which of the following must be positive?
A.sinx+tanx
B.cosx+tanx
C.sinx+cosx
D.sinx-cosx

I don't know how to do this question, what method can I use?
Thanks.

 

[dextercioby]

Sign tables for "sin" & "cos"...?The answer is "D".

Daniel.

 

[fork]

>>Sign tables for "sin" & "cos"...

Sorry, I don't understand.

 

[elessar_telkontar]

I have a mnemotecnic rule for remember the signs of the 3 basical trigonometric functions, however this is in spanish, and I can't get a english version. The rule reads:

CUST

where C is cosine S sine and T tangent, and U is a connector that has no mathematical sense (If we don't put U the rule is CST and is the same one with the U).

But the letters also has the meaning of:

C: Cuarto cuadrante (4th quadrant)
S: Segundo cuadrante (2th quadrant)
T: Tercer cuadrante (3th quadrant)

Then the rule says that

The cosine is positive in 4th quadrant
The sine is positive in 2th quadrant
The tangent is positive in 3th quadrant

The cosine, sine and tangent are positive too in the first quadrant, obviously.

 

[fork]

I get what you two mean, thanks.
A.(+)+(-)=?
B.(-)+(-)=-
C.(+)+(-)=?
D.(+)-(-)=+

So, the answer is option D, right?

 

[dextercioby]

That's right.


Daniel.

 

[jtbell]

Anyone who is using trig functions should memorize the shape of the graphs of sine, cosine, and tangent in the range of 0 to 360 degrees, showing in particular where they are zero, where they are positive and negative, and where they reach their maximum and minimum values.

With those graphs in your head, you should be able to do a problem like this one in a few seconds.