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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.

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

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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

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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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*summary of this topic*

Voice

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Home

From 4th to 1st Quadrant

» `270+theta`

→ `theta` measured with y axis

→ complementary functions

» `-theta`

→ `theta` measured with x axis

→ equivalent functions

*plain and simple summary*

nub

*plain and simple summary*

nub

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*simple steps to build the foundation*

trek

*simple steps to build the foundation*

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The results of representing trigonometric ratios of angles in 4th quadrant equivalently as trigonometric ratios of acute angle in 1st quadrant are explained.

Starting on learning representing trigonometric ratios for "Angles in 4th Quadrant". ;; The results of representing trigonometric ratios of angles in 4th quadrant equivalently as trigonometric ratios of acute angle in 1st quadrant are explained.

The angle `omega = 270+theta` is shown in the figure as point P. The similar triangle with angle theta is given by `Q(x,y)` in 1st quadrant. Note: Given `Q(x,y)`, the coordinates of `P` is `(color(coral)(P_x),color(deepskyblue)(P_y))`:

`color(coral)(P_x=y)` and `color(deepskyblue)(P_y=-x)`

What is `tan (270+theta)`?

- `y/x = tan theta`
- `(-y)/x = - tan theta`
- `x/y= cot theta`
- `x/(-y) = - cot theta`

The answer is '`(-x)/y = - cot theta`'

`tan (270+theta)` (tan of the given angle)

`quad = (P_y)/(P_x)` (by definition of `tan`)

`quad = (-x)/y` (substituting the values)

`quad = - cot theta` (equivalently in 1st quadrant.)

Note: learners can work out this for `sin` and `cos`.

For angles given as `270+theta`, the trigonometric ratios are: • `sin (270+theta) = - cos theta`

• `cos (270+theta) = sin theta`

• `tan (270+theta) = - cot theta`

The angle `omega = -theta` is shown in the figure as point P. The similar triangle with angle theta is given by `Q(x,y)` in 1st quadrant. Note: Given `Q(x,y)`, the coordinates of `P` is `(color(coral)(P_x),color(deepskyblue)(P_y))`:

`color(coral)(P_x=x)` and `color(deepskyblue)(P_y=-y)`

What is `tan (-theta)`?

- `y/x = tan theta`
- `(-y)/x = - tan theta`
- `x/y= cot theta`
- `x/(-y) = - cot theta`

The answer is '`(-y)/x = - tan theta`'

`tan (-theta)` (tan of the given angle)

`quad = (P_y)/(P_x)` (by definition of `tan`)

`quad = (-y)/x` (substituting the values)

`quad = - tan theta` (equivalently in 1st quadrant.)

Note: learners can work out this for `sin` and `cos`.

For angles given as `-theta`, the trigonometric ratios are: • `sin (-theta) = - sin theta`

• `cos (-theta) = cos theta`

• `tan (-theta) = - tan theta`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

The angle omega equals 270 plus theta is shown in the figure as point P. The similar triangle with angle theta is given by Q x y in 1st quadrant ;; Note: Given Q x y , the coordinates of P is P x = minus y and p y = x. What is tan 270 plus theta?

equals tan

y by x equals tan theta

minus tan

y by minus x equals minus tan theta

equals cot

x by y equals cot theta

minus cot

minus x by y equals minus cot theta

The answer is 'minus x by y equals minus cot theta'

For angles given as 270 plus theta, the trigonometric ratios are: sine 270 plus theta equals minus cos theta;; cos 270 plus theta equals sine theta;; tan 270 plus theta equals minus cot theta

The angle omega equals minus theta is shown in the figure as point P. The similar triangle with angle theta is given by Q x y in 1st quadrant ;; Note: Given Q x y , the coordinates of P is P x = x and p y = minus y. What is tan minus theta?

equals tan

y by x equals tan theta

minus tan

minus y by x equals minus tan theta

equals cot

x by y equals cot theta

minus cot

x by minus y equals minus cot theta

The answer is ' minus y by x equals minus tan theta'

For angles given as minus theta, the trigonometric ratios are: sine minus theta equals minus sine theta;; cos minus theta equals cos theta;; tan minus theta equals minus tan theta