nubtrek

Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

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

User Guide   

Welcome to nubtrek.

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

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.

continue

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. continue

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. continue

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. continue

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. continue

summary of this topic

Trigonometric Ratio for Angles in All Quadrants

Trigonometric Ratio for Angles in All Quadrants

Voice  

Voice  



Home



Complementary Angles 1st Quadrant


 »  `90-theta`
    →  `theta` measured with y axis
    →  complementary functions

Angles in 1st Quadrant

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

Support Nubtrek     
 

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.




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


Keep tapping on the content to continue learning.
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. trigonometric ratio of angle 90-theta 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:trigonometric ratio of angle 90-theta  • `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.

    we are not perfect yet...

    Help us improve