TRIGONOMETRIC RATIOS OF 90 DEGREE MINUS THETA
Trigonometric ratios of 90 degree minus theta is one of the branches of ASTC formula in trigonometry.
Trigonometric-ratios of 90 degree minus theta are given below.
sin (90° - θ) = cos θ
cos (90° - θ) = sin θ
tan (90° - θ) = cot θ
csc (90° - θ) = sec θ
sec (90° - θ) = csc θ
cot (90° - θ) = tan θ
Let us see, how the trigonometric ratios of 90 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
(90° - θ) falls in the first quadrant
In the first quadrant (90° - θ), all trigonometric ratios are positive.
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 90 Degree Minus Theta
Problem 1 :
Evaluate :
sin (90° - θ)
Solution :
To evaluate sin (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "sin" will become "cos".
(iii) In the I st quadrant, the sign of "sin" is positive.
Considering the above points, we have
sin (90° - θ) = cos θ
Problem 2 :
Evaluate :
cos (90° - θ)
Solution :
To evaluate cos (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "cos" will become "sin".
(iii) In the I st quadrant, the sign of "cos" is positive.
Considering the above points, we have
cos (90° - θ) = sin θ
Problem 3 :
Evaluate :
tan (90° - θ)
Solution :
To evaluate tan (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "tan" will become "cot".
(iii) In the I st quadrant, the sign of "tan" is positive.
Considering the above points, we have
tan (90° - θ) = cot θ
Problem 4 :
Evaluate :
csc (90° - θ)
Solution :
To evaluate csc (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "csc" will become "sec".
(iii) In the I st quadrant, the sign of "csc" is positive.
Considering the above points, we have
csc (90° - θ) = sec θ
Problem 5 :
Evaluate :
sec (90° - θ)
Solution :
To evaluate sec (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "sec" will become "csc".
(iii) In the I st quadrant, the sign of "sec" is positive.
Considering the above points, we have
sec (90° - θ) = csc θ
Problem 6 :
Evaluate :
cot (90° - θ)
Solution :
To evaluate cot (90° - θ), we have to consider the following important points.
(i) (90° - θ) will fall in the I st quadrant.
(ii) When we have 90°, "cot" will become "tan"
(iii) In the I st quadrant, the sign of "cot" is positive.
Considering the above points, we have
cot (90° - θ) = tan θ
Summary (90 Degree Minus Theta)
sin (90° - θ) = cos θ
cos (90° - θ) = sin θ
tan (90° - θ) = cot θ
csc (90° - θ) = sec θ
sec (90° - θ) = csc θ
cot (90° - θ) = tan θ
Apart from the stuff given in this section, if you need any other stuff in math, 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
Recent Articles
-
Volume of Cone Questions and Answers
Jan 18, 21 11:58 AM
Volume of Cone Questions and Answers
-
Volume of Cylinder Questions and Answers
Jan 18, 21 11:13 AM
Volume of Cylinder Questions and Answers
-
Examples on Volume of Cylinder
Jan 18, 21 10:20 AM
Examples on Volume of Cylinder
