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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.

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

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figure-out, &

learn.

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

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trek,

jogger,

exercise.

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*summary of this topic*

Voice

Voice

Home

Trigonometric Values : First Principles

» The angle `omega` is measured from positive x-axis

→ x and y coordinates takes sign

» `P` is in the second quadrant

→ -ve x projection

→ +ve y projection

» `Q` is in third quadrant

→ -ve: both x and y projections

» `R` is in fourth quadrant

→ +ve x projection

→ -ve y projection

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

For any angle the trigonometric values are computed using the projections of point on unit circle at the given angle on to x and y axis.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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This page explains the first principles to calculate a trigonometric ratio for a given angle. The rest of the knowledge extends the first principles to arrive at standard formulas or results.

Starting on learning "Trigonometric values for Any Angle: First Principles". ;; This page explains the first principles to calculate a trigonometric ratio for a given angle. The rest of the knowledge extends the first principles to arrive at standard formulas or results.

The angle `omega` is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. What is `tan omega`?

- `b/a`
- `b/(-a)`

The answer is '`b/(-a)`'

The trigonometric ratios are computed from the x and y axis projections.

Note that the projections are given for point on unit circle. so `sqrt(a^2 + b^2) = 1`. `sin omega = b/1`

`cos omega = (-a)/1`

`tan omega = b/(-a)`

The angle `omega` is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. What is `tan omega`?

- `b/a`
- `(-b)/(-a)`

The answer is '`(-b)/(-a)`'. Note that the sign of the numerator and denominator provide information as to if the angle is in first quadrant or 3rd quadrant.

The trigonometric ratios are computed from the x and y axis projections.

Note that the projections are given for point on unit circle. so `sqrt(a^2 + b^2) = 1`. `sin omega = (-b)/1`

`cos omega = (-a)/1`

`tan omega = (-b)/(-a)`

The angle `omega` is negative and is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. What is `tan omega`?

- `b/a`
- `(-b)/a`

The answer is '`(-b)/a`'

The trigonometric ratios are computed from the x and y axis projections.

Note that the projections are given for point on unit circle. so `sqrt(a^2 + b^2) = 1`. `sin omega = (-b)/1`

`cos omega = a/1`

`tan omega = (-b)/a`

The angle `omega = 590` is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. What is `tan omega`?

- `a/b`
- `(-b)/(-a)`

The answer is '`(-b)/(-a)`'

The trigonometric ratios are computed from the x and y axis projections. `sin omega = (-b)/1`

`cos omega = (-a)/1`

`tan omega = (-b)/(-a)`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**First Principles to find Trigonometric Ratios for any Angle: ** For the given angle, find the projections of point on unit circle at the given angle on to x and y axes. The projections are signed values. The trigonometric ratios are computed as

• `sin omega = y text( projection)`

• `cos omega = x text( projection)`

• `tan omega = (y text( projection))/(x text( projection))`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

The angle omega is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. ;; What is tan omega?

by a

b by ae

minus;-

b by minus a

The answer is 'b by minus a'

The trigonometric ratios are computed from the x and y axis projections.;; Note that the projections are given for point on unit circle. so square root a square plus b square equals 1. ;; sine omega ; equals ; b by 1 ;; divided by one is given to specify the radius of the circle. ;; cos omega ; equals ; minus a by 1 ;; tan omega ; equals ; b by minus a

The angle omega is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. ;; What is tan omega?

by a

b by a

minus;-

minus b by minus a

The answer is 'minus b by minus a' Note that the sign of the numerator and denominator provide information as to if the angle is in first quadrant or 3rd quadrant.

The trigonometric ratios are computed from the x and y axis projections.;; sine omega ; equals ; minus b by 1 ;; divided by one is given to specify the radius of the circle. ;; cos omega ; equals ; minus a by 1 ;; tan omega ; equals ; minus b by minus a

The angle omega is negative and is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. ;; What is tan omega?

by a

b by a

minus;-

minus b by a

The answer is ' minus b by a'

The trigonometric ratios are computed from the x and y axis projections. ;; sine omega ; equals ; minus b by 1 ;; cos omega ; equals ; a by 1 ;; tan omega ; equals ; minus b by a

The angle omega equals 590 is shown in the figure. The magnitude of projections on x axis and y axis is given as a and b. ;; What is tan omega?

by b;a by

a by b

minus;-

minus b by minus a

The answer is 'minus b by minus a'

The trigonometric ratios are computed from the x and y axis projections.;; sine omega ; equals ; minus b by 1 ;; cos omega ; equals ; minus a by 1 ;; tan omega ; equals ; minus b by minus a

For any angle the trigonometric values are computed using the projections of point on unit circle at the given angle on to x and y axis.

First Principles to find Trigonometric Ratios for any angle: ;; For the given angle, find the projections of point on unit circle at the given angle on to x and y axes. The projections are signed values. The trigonometric ratios are computed as ;; sine omega is y projection ;; cos omega is x projection;; tan omega is y projection by x projection.