TRIGONOMETRIC RATIOS OF 270 DEGREE MINUS THETA

About "Trigonometric ratios of 270 degree minus theta"

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

Trigonometric-ratios of 270 degree minus 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 minus 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 minus theta falls in the third quadrant

In the third quadrant (270° degree minus theta), tan and cot 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 using ASTC formula

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 III rd quadrant.

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

(iii)  In the III rd 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 III rd quadrant.

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

(iii)  In the III rd quadrant, the sign of "cos" is negative.

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 III th quadrant.

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

(iii)  In the III rd quadrant, the sign of "tan" is positive.

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 III rd quadrant.

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

(iii)  In the III rd 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 III rd quadrant.

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

(iii)  In the III rd quadrant, the sign of "sec" is negative.

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 III rd quadrant.

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

(iii)  In the III rd quadrant, the sign of "cot" is positive.

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

After having gone through the stuff given above, we hope that the students would have understood "Trigonometric ratios of 270 degree minus theta"

If you want to know more about "Trigonometric ratios of 270 degree minus theta", please click here

Apart from "Trigonometric ratios of 270 degree minus theta", if you need any other stuff in math, please use our google custom search here.

You can also visit our 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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 