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Thought-Process to Discover Knowledge

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

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

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

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User Guide

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.

User Guide

nub is the simple explanation of the concept.

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

User Guide

trek is the step by step exploration of the concept.

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.

User Guide

jogger provides the complete mathematical definition of the concepts.

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.

User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### Basics of Trigonometry

Voice

Voice

Home

Trigonometric Ratios: Triangle form

»  similar right-triangle

→  given angle theta

→  position of right-angle with reference to given angle

→  hypotenuse with reference to the right-angle

→  position of a side with reference to the given angle : opposite-side

→  position of another side with reference to the given angle : adjacent-side

»  Trigonometric Ratios
→  sin theta = text(opposite)/text(hypotenuse)
→  cos theta = text(adjacent)/text(hypotenuse)
→  tan theta = text(opposite)/text(adjacent) quad = (sin theta)/(cos theta)

Note: In advanced trigonometry, a general form "trigonometric values on unit circle" will be introduced.

### Triangular Form of Trigonometric Ratios

plain and simple summary

nub

plain and simple summary

nub

dummy

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, the trigonometric ratios defined in triangular form is revised. Note: The trigonometric ratios are also called trigonometric values and are defined in unit circle form. This will be explained in advanced trigonometry.

Keep tapping on the content to continue learning.
Starting on learning "Triangular Form of trigonometric Ratios". ;; Note: The trigonometric ratios are also called trigonometric values and are defined in unit circle form. This will be explained in advanced trigonometry.

Which side is the hypotenuse?

• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(PR)'

Which side is the opposite side to /_theta?

• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(QR)'

Which side is the adjacent side to /_theta?

• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(PQ)'

Which side is the opposite side to /_theta?

• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(PQ)'

Which side is the adjacent side to /_theta?

• bar(PQ)
• bar(QR)
• bar(PR)

The answer is 'bar(QR)'

Which side is the hypotenuse?

• bar(AB)
• bar(BC)
• bar(AC)

The answer is 'bar(AB)'

Which side is the hypotenuse?

• bar(AB)
• bar(BC)
• bar(AC)

The answer is 'bar(AC)'

Which side is the opposite side to /_theta?

• bar(AB)
• bar(BC)
• bar(AC)

The answer is 'bar(BC)'

Which side is the adjacent side to /_theta?

• bar(AB)
• bar(BC)
• bar(PR)

The answer is 'bar(BC)'

What is sin theta?

• text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)

The answer is 'text(opposite)/text(hypotenuse)'

What is cos theta?

• text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)

The answer is 'text(adjacent)/text(hypotenuse)'

What is tan theta?

• text(opposite)/text(hypotenuse)
• text(adjacent)/text(hypotenuse)
• text(opposite)/text(adjacent)

The answer is 'text(opposite)/text(adjacent)'

Which of the following is equivalently tan theta?

• 1/ (sin theta)
• 1/(cos theta)
• (sin theta)/(cos theta)

The answer is '(sin theta)/(cos theta)'

Revising the definition of trigonometric ratios

sin theta = text(opposite)/text(hypotenuse)

cos theta = text(adjacent)/text(hypotenuse)

tan theta = text(opposite)/text(adjacent)

What is 1/(cos theta)?

• text(hypotenuse)/text(opposite)
• text(hypotenuse)/text(adjacent)

The answer is 'text(hypotenuse)/text(adjacent)'

1/(cos theta) is called as 'sec theta'.

sec theta

quad quad = text(hypotenuse)/text(adjacent)

quad quad = 1/ (cos theta)

What is 1/(sin theta)?

• text(hypotenuse)/text(opposite)
• text(hypotenuse)/text(adjacent)

The answer is 'text(hypotenuse)/text(opposite)'

1/(sin theta) is called as 'text(cosec) theta' or 'csc theta'.

text(cosec) theta or csc theta

quad quad = text(hypotenuse)/text(opposite)

quad quad = 1/ (sin theta)

What is 1/(tan theta)?

• text(opposite)/text(adjacent)
• text(adjacent)/text(opposite)

The answer is 'text(adjacent)/text(opposite)'

1/(tan theta) is called as 'cot theta'.

text(tan) theta

quad quad = text(adjacent)/text(opposite)

quad quad = 1/ (tan theta)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Trigonometric Ratios:
sin theta = text(opposite)/text(hypotenuse)

cos theta = text(adjacent)/text(hypotenuse)

tan theta = text(opposite)/text(adjacent)

sec theta = text(hypotenuse)/text(adjacent)

text(cosec) theta = text(hypotenuse)/text(opposite)

cot theta = text(adjacent)/text(opposite)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

Which side is the hypotenuse?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P R'
Which side is the opposite side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line Q R'
Which side is the adjacent side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P Q'
Which side is the opposite side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line P Q'
Which side is the adjacent side to the angle theta?
PQ
line P Q
QR
line Q R
PR
line P R
The answer is 'line Q R'
Which side is the hypotenuse?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line A B'
Which side is the hypotenuse?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line A C'
Which side is the opposite side to the angle theta?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line B C'
Which side is the adjacent side to the angle theta?
AB
line A B
BC
line B C
AC
line A C
The answer is 'line B C'
What is sine theta?
opposite
opposite by hypotenuse
The answer is 'opposite by hypotenuse'
What is cause theta?
opposite
opposite by hypotenuse
What is tan theta?
opposite by hypotenuse
opposite by hypotenuse
Which of the following is equivalently tan theta?
one by; sine
one by sine theta
cos;cause;
one by cause theta
sine theta by cause theta;sine by cause; theta by
sine theta by cause theta
The answer is 'sine theta by cause theta'
Revising the definition of trigonometric ratios. ;; sine theta equals opposite side by hypotenuse. ;; cause theta equals adjacent side by hypotenuse. ;; tan theta equals opposite side by adjacent side
What is one by cause theta?
opposite
hypotenuse by opposite
one by cause theta is called as 'secant theta'. ;; secant theta equals hypotenuse by adjacent side. ;; equals one by cause theta
What is one by sine theta?
opposite
hypotenuse by opposite
The answer is 'hypotenuse by opposite'
one by sine theta is called as 'co-secant theta'. ;; co-secant theta equals hypotenuse by opposite side. ;; equals one by sine theta
What is one by tan theta?
one by tan theta is called as 'cot theta'. ;; cot theta equals adjacent side by opposite side. ;; equals one by tan theta
Summary of trigonometric ratios. ;; sine theta equals opposite side by hypotenuse. ;; cause theta equals adjacent side by hypotenuse. ;; tan theta equals opposite side by adjacent side. ;; secant theta equals hypotenuse by adjacent side. ;; co-secant theta equals hypotenuse by opposite side. ;; cot theta equals adjacent side by opposite side

we are not perfect yet...