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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

*summary of this topic*

Voice

Voice

Home

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

*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.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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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.

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. 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`. 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`. 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

*your progress details*

Progress

*About you*

Progress

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.