# TRIGONOMETRIC RATIOS OF 270 DEGREE PLUS THETA

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 formula 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.

## Important Conversions

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.

## Evaluation of Trigonometric Ratios of 270 Degree Plus Theta

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 IVth quadrant.

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

(iii)  In the IVth 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 IVth quadrant.

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

(iii)  In the IVth 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 IVth quadrant.

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

(iii)  In the IVth 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 IVth quadrant.

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

(iii)  In the IVth 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 IVth quadrant.

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

(iii)  In the IVth 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 IVth quadrant.

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

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

Considering the above points, we have

cot (270° + θ)  =  - tan θ

## Summary (270 Degree + 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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

## Recent Articles

1. ### Adaptive Learning Platforms

May 26, 23 12:27 PM

Adaptive Learning Platforms: Personalized Mathematics Instruction with Technology

Read More

2. ### Simplifying Expressions with Rational Exponents Worksheet

May 21, 23 07:40 PM

Simplifying Expressions with Rational Exponents Worksheet

Read More

3. ### Simplifying Rational Expressions Worksheet

May 20, 23 10:53 PM

Simplifying Rational Expressions Worksheet

Read More