# Where trig functions are positive and negative?

The distance from a point to the origin is always positive, but the signs of the x and y coordinates may be positive or negative. Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values.

## Where are the trig functions negative?

Based on the unit circle, the negative angle identities (also called "odd/even" identities) tell you how to find the trig functions at -x in terms of the trig functions at x. In other words, they relate trig values at opposite angles x and -x. For example, sin(-x) = -sin(x), cos(-x) = cos(x), and tan(-x) = -tan(x).

## What quadrants is each trig functions positive and negative?

• In Quadrant I both x and y are positive,
• in Quadrant II x is negative (y is still positive),
• in Quadrant III both x and y are negative, and.
• in Quadrant IV x is positive again, and y is negative.

## What quadrants are the 6 trig functions positive and negative?

It follows that:
• sine is positive in quadrants I and II: points above the x -axis have positive y -values.
• sine is negative in quadrants III and IV: points below the x -axis have negative y -values.
• cosine is positive in quadrants I and IV: ...
• cosine is negative in quadrants II and III:

## Where is sin positive and negative?

for angles with their terminal arm in Quadrant II, since sine is positive and cosine is negative, tangent is negative. for angles with their terminal arm in Quadrant III, since sine is negative and cosine is negative, tangent is positive.

## Trigonometry - The signs of trigonometric functions

45 related questions found

### How do you know when a sin is negative?

The sine ratio is y/r, and the hypotenuse r is always positive. So the sine will be negative when y is negative, which happens in the third and fourth quadrants.

### Is Tan positive or negative?

In the second quadrant (II), sine (and cosec) are positive. In the third quadrant (III), tan (and cotan) are positive. In the fourth quadrant (IV), cos (and sec) are positive. These just follow from the sign (+ or -) of x or y for each quadrant, as we saw above.

### What quadrant is sin positive?

• All trig functions (sin, cos, tan, sec, csc, cot) are positive in the first quadrant.
• Sine is positive in the second quadrant.
• Tangent is positive in the third quadrant.
• Cosine is positive in the fourth quadrant.

### Where is csc negative?

Since − 5 π 6 \displaystyle -\frac{5\pi }{6} −65π​ is in the third quadrant, where both x and y are negative, cosine, sine, secant, and cosecant will be negative, while tangent and cotangent will be positive.

### What is negative cosecant?

Comparing sine functions

The comparison of both cosecant functions disclose that cosecant of negative angle equals to negative of cosecant of positive angle. ⁡ ⁡ ∴ csc ⁡ ⁡ This negative identity is called cosecant of negative angle identity and frequently used as a formula in trigonometric mathematics.

### What quadrants is sine negative?

Trigonometric functions sine and cosine are both positive in first quadrant but in third quadrant both are negative. Hence in these two quadrants they have same sign. However, in second quadrant while sine is positive, cosine is negative. And in fourth quadrant, cosine is positive and sine is negative.

### What is Cosec in math?

Cosecant is one of the six trigonometric ratios which is also denoted as cosec or csc. The cosecant formula is given by the length of the hypotenuse divided by the length of the opposite side in a right triangle.

### What are the symbols in trigonometry?

Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

### What happens when an angle is negative?

2 Answers. Negative angles has to do with the direction of rotation that you consider in order to measure angles. Normally you start counting your angles from the positive side of the x axis in an anti-clockwise direction of rotation: ... negative is the equivalent of these words in math.

### What is negative angle identity?

Negative angle identities are trigonometric identities that show the relationships between trigonometric functions when we take the trigonometric function of a negative angle. These identities are as follows: sin(-x) = -sin(x) cos(-x) = cos(x)

### Is there a negative angle?

Angles are measured in degrees. One complete rotation is measured as 360°. Angle measure can be positive or negative, depending on the direction of rotation. ... Positive angles (Figure a) result from counterclockwise rotation, and negative angles (Figure b) result from clockwise rotation.

### Is CSC positive or negative?

Sine and cosecant are positive in Quadrant 2, tangent and cotangent are positive in Quadrant 3, and cosine and secant are positive in Quadrant 4.

### Can a tangent be negative?

The tangent function is negative whenever sine or cosine, but not both, are negative: the second and fourth quadrants. Tangent is also equal to the slope of the terminal side.

### Is quadrant 3 positive or negative?

In Quadrant I, both the x– and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV, x is positive but y is negative.

### What are the 4 quadrants?

The x and the y axes divide the plane into four graph quadrants. These are formed by the intersection of the x and y axes and are named as: Quadrant I, II, III, and IV. In words, we call them first, second, third, and fourth quadrant.

### What quadrant is sin less than 0?

The only quadrant where x is positive, so cos(x)>0 , and y is negative, so sin(x)<0 , is Quadrant IV .

### Where is tan equal to?

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x . The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x .

### Is tan always positive?

This can be summed up as follows: In the fourth quadrant, Cos is positive, in the first, All are positive, in the second, Sin is positive and in the third quadrant, Tan is positive. This is easy to remember, since it spells "cast".

### Where is tan less than 0?

Therefore: In Quadrant IV, cos(θ) > 0, sin(θ) < 0 and tan(θ) < 0 (Cosine positive). The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.