# Maths: Trigo - Which is Positive When 90° < x < 180°?

• fork
In summary, the answer to the question of which of the following must be positive if 90 degree < x < 180 degree is option D, sinx-cosx. To solve this type of problem, it is helpful to have a mnemonic rule or to memorize the shape of the graphs of sine, cosine, and tangent in the range of 0 to 360 degrees, including where they are zero, positive, negative, and reach their maximum and minimum values. With this knowledge, it is possible to quickly solve problems involving trigonometric functions.
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.

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

Daniel.

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

Sorry, I don't understand.

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:

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.

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

So, the answer is option D, right?

That's right.

Daniel.

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.

## 1. What is the range of values for x in trigonometry when 90° < x < 180°?

The range of values for x in trigonometry when 90° < x < 180° is from 90° to 180°. This means that x can take on any value between 90° and 180°, but not including these two values.

## 2. Which trigonometric functions are positive in the range of 90° < x < 180°?

In this range, the sine and cosecant functions are positive. This means that the ratio of the opposite side to the hypotenuse is positive, as well as the ratio of the hypotenuse to the adjacent side.

## 3. How do you find the values of trigonometric functions in the range of 90° < x < 180°?

To find the values of trigonometric functions in this range, you can use a calculator or reference table. Simply input the angle in degrees and the calculator will give you the value of the function. Alternatively, you can use the unit circle to find the values by hand.

## 4. What is the relationship between the values of trigonometric functions in the range of 90° < x < 180° and the values in other quadrants?

The values of trigonometric functions in this range are the same as the values in the second quadrant (90° < x < 180°). However, the signs of these values are different. In the second quadrant, only the sine and cosecant functions are positive, while in the third quadrant (180° < x < 270°), only the tangent and cotangent functions are positive.

## 5. Why is it important to know the values of trigonometric functions in the range of 90° < x < 180°?

Knowing the values of trigonometric functions in this range is important for solving problems involving angles in the second quadrant, as well as for understanding the relationships between the values in different quadrants. This knowledge is also essential for further applications of trigonometry, such as in physics and engineering.

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