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Thought-Process to Discover Knowledge

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User Guide

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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.

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User Guide

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User Guide

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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

### Trigonometric Basic Identities

Voice

Voice

Home

Complementary Angles

»  Quickly follow that the adjacent and opposite sides swap for complementary angles... no need to memorize.

sin(90-theta) = cos theta
cos(90-theta) = sin theta
tan(90-theta) = cot theta

csc(90-theta) = sec theta
sec(90-theta) = csc theta
cot(90-theta) = tan theta

### Trigonometric Ratios for Complementary Angles

plain and simple summary

nub

plain and simple summary

nub

dummy

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

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

csc(90-theta) = sec theta
sec(90-theta) = csc theta

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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The relationship between trigonometric ratios of an angle and its complementary angle is explained.

Keep tapping on the content to continue learning.
Starting on learning "Trigonometric Ratios for Complementary Angles". ;; The relationship between trigonometric ratios of an angle and its complementary angle is explained.

What is the complementary angle of theta?

• angle that completes theta to a right angle
• 90-theta
• both the above

The answer is 'both the above'

In the right angled triangle shown in figure, if /_P = theta then what is /_R ?

• complementary angle of theta
• 90-theta
• both the above

The answer is 'both the above'

In the right angled triangle shown in figure, what is the opposite side for /_P  ?

• PQ
• QR

In the right angled triangle shown in figure, what is the adjacent side for /_R  ?

• PQ
• QR

A right angled triangle is shown in figure. Opposite of /_theta = Adjacent of /_(90-theta)
Adjacent of /_theta = Opposite of /_(90-theta)

The trigonometric ratios of 90-theta can be expressed in terms of trigonometric ratios of theta or vice versa. From the figure
sin theta = (RQ)/(PR)
cos theta = (PQ)/(PR)
sin (90-theta) = (PQ)/(PR)
cos (90-theta) = (RQ)/(PR)

Comparing the above, it is concluded that
sin (90-theta) = cos theta
cos (90-theta) = sin theta

The trigonometric ratios of 90-theta can be expressed in terms of trigonometric ratios of theta or vice versa. From the figure
tan theta = (RQ)/(PQ)
cot theta = (PQ)/(RQ)
tan (90-theta) = (PQ)/(RQ)
cot (90-theta) = (RQ)/(PQ)

Comparing the above, it is concluded that
tan (90-theta) = cot theta
cot (90-theta) = tan theta

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Trigonometric Ratios for Complementary Angles:
sin(90-theta) = cos theta
cos(90-theta) = sin theta

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

csc(90-theta) = sec theta
sec(90-theta) = csc theta

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Which of the following equals sin 36?

• cos 54
• tan 54
• sec 54
• sin 54

The answer is 'cos 54'

(tan 75) / (cot 15) = ?

• tan^2 75
• 1

The answer is '1' As cot 15 =tan(90-15) =tan 75.

Which of the following equals sin 36 - cos 36 + sin 54?

• sin 54
• sin 36

The answer is 'sin 36'.

Progress

Progress

What is the complementary angle of theta ?
angle;completes;right
angle that completes theta to a right angle
90;minus
90 minus theta
both;above
both the above
The answer is 'both the above'
In the right angled triangle shown in figure, if angle p equals theta, then what is angle R?
angle;complementary
complementary angle of theta
90;minus
90 minus theta
both;above
both the above
The answer is 'both the above'
In the right angled triangle shown in figure, what is the opposite side for angle p?
p;pee
P Q
r;are;or
Q R
In the right angled triangle shown in figure, what is the adjacent side for angle r?
p;pee
P Q
r;are;or
Q R
A right angled triangle is shown in figure. Opposite of angle theta equals adjacent of angle 90 minus theta. ;; Adjacent of angle theta equals opposite of angle 90 minus theta.
The trigonometric ratios of 90 minus theta, can be expressed in terms of trigonometric ratios of theta or vice versa. ;; From the figure, sine theta = R Q by P R ;; cos theta = P Q by P R;; sine 90 minus theta = p Q by P R ;; cos 90-theta
Trigonometric Ratios for Complementary Angles: sine 90 minus theta equals cos theta;; cos 90 minus theta equals sine theta.
Trigonometric ratios of complementary angles are given
The trigonometric ratios of 90 minus theta, can be expressed in terms of trigonometric ratios of theta or vice versa. ;; From the figure, sine theta = R Q by P R ;; cos theta = P Q by P R;; sine 90 minus theta = p Q by P R ;; cos 90-theta
Trigonometric Ratios for Complementary Angles: tan 90 minus theta equals cot theta;; cot 90 minus theta equals tan theta.
Trigonometric ratios of complementary angles are given
Trigonometric Ratios for Complementary Angles: co-secant 90 minus theta equals secant theta;; secant 90 minus theta equals co-secant theta.
Trigonometric ratios of complementary angles are given
Which of the following equals sine 36?
cos
cos 54
tan
tan 54
secant
secant 54
sine
sine 54
tan 75 divided by cot 15 equals?
tan
tan squared 75
1
1
The answer is "1". As cot 15 = tan 90 minus 15 = tan 75.
Which of the following equals sine 36 minus cos 36 plus sine 54?
54
sine 54
36
sine 36