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Trigonometric Ratios for Standard Angles

Trigonometric Ratios for Standard Angles

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Standard Angles


 »  0 : minimum possible angle
    →  opposite side is 0


 »  90 : Maximum possible angle
    →  opposite side equals hypotenuse


 »  45 : isosceles right-triangle
    →  opposite and adjacent sides equal


 »  30 and 60 : Derived from equilateral triangle
    →  one side is half of hypotenuse

Understanding Standard Angles

plain and simple summary

nub

plain and simple summary

nub

dummy

The standard angles for which the trigonometric ratios are in the form of simple ratios, are derived from equilateral, isosceles, and `0^@` triangles. Use the known properties of these triangles to compute the trigonometric functions.

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simple steps to build the foundation

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What are the standard angles for which trigonometric ratios are defined? These angles are chosen because of some pattern or properties. This page explains the reason why some angles are special.


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Starting on "Understanding Standard Angles". ;; What are the standard angles for which trigonometric ratios are defined? These angles are chosen because of some pattern or properties. This page explains the reason why some angles are special.

What is the value of `sin 1^@`? Can you memorize trigonometric ratios for all angles?

  • `0.0175`
  • `0.0157`
  • one cannot memorize all values of `sin theta`.

The answer is 'one cannot memorize all values of `sin theta`'.

For which angles can students work out values of trigonometric ratios `sin`, `cos`, and `tan`?

  • for the angles for which the ratio between two sides of triangles can be computed using only given angle.
  • For none

The answer is 'for the angles for which the ratio between two sides of triangles can be computed using only given angle'

In which of the following, can the ratio between two sides of triangles be computed?

  • equilateral triangles
  • isosceles triangles
  • triangles with one angle `0^@`
  • all the above

The answer is 'all the above'

The equilateral triangle is split into two right angled triangles as shown in the figure. The hypotenuse `bar(OP) = 1`. Then the side `bar(OQ) = 1/2`. The other side is to be computed using Pythagoras Theorem. trigonometry standard angles from equilateral triangles What standard angles can be derived from equilateral triangles?

  • `60^@`
  • `30^@`
  • both the above

The answer is 'both the above'

The two sides of the isosceles right angled triangle are same and the hypotenuse is `1`.trigonometry standard angles from isosceles right angled triangles What standard angles can be derived from isosceles right-angled-triangles?

  • `0^@`
  • `45^@`
  • `90^@`

The answer is '`45^@`'

The figure shows a triangle `Delta OPQ` with `/_P = 0^@`. Imagine the `bar(PR)` moves towards `bar(PO)` and forms the triangle where point `R` meets point `O`. trigonometry standard angles from triangle with 0 degree What standard angles can be derived from a right-angled triangle with one of the angles `0^@`?

  • `0^@`
  • `90^@`
  • both the above

The answer is 'both the above'

What does 'standard' mean?

  • common and established as norm
  • special and distinctively specified

Answer is 'common and established as norm'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Trigonometric Ratios for Standard Angles:

 •  `0^@` and `90^@` : right-angled-triangle with two sides `1` and the third side `0`.

 •  `45^@` : isosceles right-angled triangle.

 •  `30^@` and `60^@` : half of equilateral triangle making a right-angled-triangle.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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What is the value of sine 1 degree? ;; Can you memorize trigonometric ratios for all angles?
seven five
0 point 0 one seven five
five seven
0 point 0 one five seven
memorize;sine;theta;values
one cannot memorize all values of sine theta.
The answer is 'one cannot memorize all values of sine theta.'
For which angles can students work out values of trigonometric ratios ;; sine, cos, and tan?
ratio;between;angles;sides
for the angles for which the ratio between two sides of triangles can be computed using only given angle.
none
For none
The answer is 'for the angles for which the ratio between two sides of triangles can be computed using only given angle'
In which of the following, can the ratio between two sides of triangles be computed?
equilateral
equilateral triangles
isosceles
isosceles triangles
zero;0;degree
triangles with one angle 0 degree
all; above
all the above
The answer is 'all the above'
The equilateral triangle is split into two right angled triangles as shown in the figure. The hypotenuse O P ; = ; 1. Then the side line O Q ; = ; half . The other side is to be computed using Pythagoras Theorem.;; What standard angles can be derived from equilateral triangles?
60;sixty
60 degree
30;thirty
30 degree
both;above
both the above
The answer is 'both the above'
The two sides of the isosceles right angled triangle are same and the hypotenuse is 1. What standard angles can be derived from isosceles right-angled-triangles? ;
0;zero
0 degree
45;forty;five
45 degree
90;ninety
90 degree
The answer is '45 degree'
The figure shows a triangle O P Q with angle P = 0 degree. Imagine the line P R moves towards line P O and forms the triangle where point R meets point O. What standard angles can be derived from a right-angled triangle with one of the angles 0 degree? ;
0;zero
0 degree
90;ninety
90 degree
both;above
both the above
The answer is 'both the above'
What does 'standard' mean?
common;established
common and established as norm
special;specified;distinctively
special and distinctively specified
Answer is 'common and established as norm'
The standard angles for which the trigonometric ratios are in the form of simple ratios are derived from equilateral, isosceles, and 0 degree triangles. Use the known properties of these triangles to compute the trigonometric functions.
Trigonometric Ratios for Standard Angles: ;; 0 degree and 90 degree ;; right-angled-triangle with two sides 1 and the third side 0. ;; 45 degree ;; isosceles right-angled triangle. ;; 30 degree and 60 degree ;; half of equilateral triangle making a right-angled-triangle.

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