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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

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

Complementary Angles 1st Quadrant

» `90-theta`

→ `theta` measured with y axis

→ complementary functions

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

For angles measured in reference to x axis, the trigonometric ratios remain the same when equivalently represented in the 1st quadrant.

For angles measured in reference to y axis, the trigonometric ratios are equivalently complementary ratios in the 1st quadrant.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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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 = 90-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 (90-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 (90-theta)` (tan of the given angle)

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

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

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

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

For angles given as `90-theta`, the trigonometric ratios are: • `sin (90-theta) = cos theta`

• `cos (90-theta) = sin theta`

• `tan (90-theta) = cot theta`

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Trigonometric Ratios in 1st Quadrant: **

For Angles in reference to x-axis:

`sin(180+-theta) = -+sin theta`

`cos(180+-theta) = -cos theta`

`tan(180+-theta) = +-tan theta`

`sin(-theta) = -sin theta`

`cos(-theta) = cos theta`

`tan(-theta) = -tan theta`

For Angles in reference to y-axis:

`sin(90+-theta) = cos theta`

`cos(90+-theta) = -+sin theta`

`tan(90+-theta) = -+cot theta`

`sin(270+-theta) = -cos theta`

`cos(270+-theta) = sin theta`

`tan(270+-theta) = -tan theta`

*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 90 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 = y and p y = x. What is tan 90 minus 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 ' x by y equals cot theta'

For angles given as 90 minus theta, the trigonometric ratios are: sine 90 minus theta equals cos theta;; cos 90 minus theta equals sine theta;; tan 90 minus theta equals cot theta

For angles measured in reference to x axis, the trigonometric ratios remain the same when equivalently represented in the 1st quadrant. ;; For angles measured in reference to y axis, the trigonometric ratios are equivalently complementary ratios in the 1st quadrant.

For angles in reference to x axis; the trigonometric ratios sine, cos, tan remain the same as sine, cos, tan when equivalently represented in the first quadrant.;; For angles in reference to y axis; the trigonometric ratios sine, cos, tan are equivalently complementary ratios cos, sine, cot when equivalently represented in the first quadrant.