Trigonometric ratios of 270 degree plus theta is one of the branches of ASTC formula in trigonometry.

Trigonometric-ratios of 270 degree plus theta are given below.

sin (270° + θ) = - cos θ

cos (270° + θ) = sin θ

tan (270° + θ) = - cot θ

csc (270° + θ) = - sec θ

sec (270° + θ) = cos θ

cot (270° + θ) = - tan θ

Let us see, how the trigonometric ratios of 270 degree plus theta are determined.

To know that, first we have to understand ASTC formula.

The ASTC formula can be remembered easily using the following phrases.

**"All Sliver Tea Cups" **

or

**"All Students Take Calculus"**

ASTC formla has been explained clearly in the figure given below.

More clearly

From the above picture, it is very clear that the angle 270 degree plus theta falls in the fourth quadrant.

In the fourth quadrant (270° degree plus theta), cos and sec are positive and other trigonometric ratios are negative.

When we have the angles 90° and 270° in the trigonometric ratios in the form of

(90° + θ)

(90° - θ)

(270° + θ)

(270° - θ)

We have to do the following conversions,

sin θ <------> cos θ

tan θ <------> cot θ

csc θ <------> sec θ

For example,

sin (270° + θ) = - cos θ

cos (90° - θ) = sin θ

For the angles 0° or 360° and 180°, we should not make the above conversions.

**Problem 1 :**

Evaluate :

sin (270° + θ)

**Solution :**

To evaluate sin (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "sin" will become "cos"

(iii) In the IV th quadrant, the sign of "sin" is negative.

Considering the above points, we have

sin (270° + θ) = - cos θ

**Problem 2 :**

Evaluate :

cos (270° + θ)

**Solution :**

To evaluate cos (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "cos" will become "sin"

(iii) In the IV th quadrant, the sign of "cos" is positive.

Considering the above points, we have

cos (270° + θ) = sin θ

**Problem 3 :**

Evaluate :

tan (270° + θ)

**Solution :**

To evaluate tan (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "tan" will become "cot"

(iii) In the IV th quadrant, the sign of "tan" is negative.

Considering the above points, we have

tan (270° + θ) = - cot θ

**Problem 4 :**

Evaluate :

csc (270° + θ)

**Solution :**

To evaluate csc (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "csc" will become "sec"

(iii) In the IV th quadrant, the sign of "csc" is negative.

Considering the above points, we have

csc (270° + θ) = - sec θ

**Problem 5 :**

Evaluate :

sec (270° + θ)

**Solution :**

To evaluate sec (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "sec" will become "csc"

(iii) In the IV th quadrant, the sign of "sec" is positive.

Considering the above points, we have

sec (270° + θ) = csc θ

**Problem 6 :**

Evaluate :

cot (270° + θ)

**Solution :**

To evaluate cot (270° + θ), we have to consider the following important points.

(i) (270° + θ) will fall in the IV th quadrant.

(ii) When we have 270°, "cot" will become "tan"

(iii) In the IV th quadrant, the sign of "cot" is negative.

Considering the above points, we have

cot (270° + θ) = - tan θ

sin (270° + θ) = - cos θ

cos (270° + θ) = sin θ

tan (270° + θ) = - cot θ

csc (270° + θ) = - sec θ

sec (270° + θ) = cos θ

cot (270° + θ) = - tan θ

Apart from the stuff given in this section, if you need any other stuff in math, please please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**