**Signs of trigonometric function theta:** **If theta θ** is not a** quadrant angle**, then it will lie in a** particular quadrant**. Because **r = √ x²+y² is always positive**, it follows that the **sign of the trigonometric** function can be found if the **quadrant of θ** is known.

** Signs of trigonometric function theta laws:**

**(1) First quadrant sign:**

If theta lies in quadrant 1,then a point p(x, y) on its **terminal side** has both **x, y co-ordinates +time.**

.

Resultant: All trigonometric functions are **positive** in **first quadrant**.

**(2) Second quadrant sign:**

If theta lies in **quadrant ii**, then a point **p(x, y)** on its **terminal side** has **negative x** – co-ordinate and positive **y-co-ordinate.**

**Resultant sign:**

sin θ = y / r =positive

cos θ = x / r = negative < 0 (because adjacent side is negative) cos θ always lies on x-axis.

Tan θ = y / x = negative <0 (because one of the sign x-axis is negative)

**(3) Third quadrant sign:**

If theta lies in **quadrant iii**, then a point **p(x, y)** on its **terminal side** has **negative x** – co-ordinate and negative **y-co-ordinate.**

**Resultant sign:**

sin θ = y / r =negative <0 (because arm y is negative)

cos θ = x / r = negative < 0 (because adjacent side x-axis is negative) cos θ always lies on x-axis.

Tan θ = y / x = positive >0 (because two negative sign cancel each other).

**(4) Fourth quadrant sign:**

If theta lies in **quadrant iv**, then a point **p(x, y)** on its **terminal side** has positive **x co-ordinate** and negative **y-co-ordinate.**

**Resultant sign:**

sin θ = y / r =negative < 0 (because arm y is negative)

cos θ = x / r = positive > 0 (because adjacent side is positive) cos θ always lies on x-axis.

Tan θ = y / x = negative <0 (because one of the sign y-axis is negative).

**RELATED POST:**

**Trigonometric identities of any real number theta****circular radius of length theta****Sexagesimal system Degree minute second**