Find the value of tan 60" 25 - cos 49° 20
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Chapter 8 Class 10 Introduction to Trignometry Concept wise Trignometric ratios of Specific Angles - Evaluating
What is value of sin, cos, tan at 0, 30, 45, 60 & 90 degree?
Last updated at Feb. 27, 2019 by Teachoo
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What is value of sin 30?
What about cos 0?
and sin 0?
How do we remember them?
Let's learn how. We will discuss what are different values of sin, cos, tan, cosec, sec, cot at 0, 30, 45, 60 and 90 degrees and how to memorise them.
So, we have to fill this table
Trigonometry Table - unfilled.jpg
How to find the values?
To learn the table, we should first know how sin cos tan are related
We know that
tan θ = sin θ/cosθ
sec θ = 1/cos θ
cosec θ = 1/sin θ
cot θ = 1/cot θ
Now let us discuss different values
For sin
For memorising sin 0°, sin 30°, sin 45°, sin 60° and sin 90°
We should learn it like
sin 0° = 0
sin 30° = 1/2
sin 45° = 1/√2
sin 60° = √3/2
sin 90° = 1
So, our pattern will be like
0, 1/2, 1/√2, √3/2, 1
Trigonometry Table - sin.jpg
For cos
For memorising cos 0°, cos 30°, cos 45°, cos 60° and cos 90°
Cos is the opposite of sin.
We should learn it like
cos 0° = sin 90° = 1
cos 30° = sin 60° = √3/2
cos 45° = sin 45° = 1/√2
cos 60° = sin 30° = 1/2
cos 90° = sin 0° = 0
So, for cos, it will be like
1, √3/2, 1/√2, 1/2, 0
Trigonometry Table - cos.jpg
For tan
We know that tan θ = sin θ /cos θ
So, it will be
tan 0° = sin 0° / cos 0° = 0/1 = 0
tan 30° = sin 30° / cos 30° = (1/2)/ (√3/2) = 1/√3
tan 45° = sin 45° / cos 45° = (1/√2)/ (1/√2) = 1
tan 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3
tan 90° = sin 90° / cos 90° = 1/0 = Not Defined = ∞
So, for tan, it is
0, 1/√3, 1, √3, ∞
Trigonometry Table - tan.jpg
For cosec
We know that
cosec θ = 1/sin θ
For sin, we know
0, 1/2, 1/√2, √3/2, 1
So, for cosec it will be
cosec 0° = 1 / sin 0° = 1/0 = Not Defined = ∞
cosec 30° = 1 / sin 40° = 1/(1/2) = 2
cosec 45° = 1 / sin 45° = 1/(1/√2) = √2
cosec 60° = 1 / sin 60° = 1/(√3/2) = 2/√3
cosec 90° = 1 / sin 90° = 1/1 = 1
So, for cosec, it is
∞, 2, √2, 2/√3, 1
Trigonometry Table - cosec csc.jpg
For sec
We know that
sec θ = 1/cos θ
For cos, we know
1, √3/2, 1/√2, 1/2, 0
So, for sec it will be
sec 0° = 1 / cos 0° = 1/1 = 1
sec 30° = 1 / cos 40° = 1/(√3/2) = 2/√3
sec 45° = 1 / cos 45° = 1/(1/√2) = √2
sec 60° = 1 / cos 60° = 1/(1/2) = 2
sec 90° = 1 / cos 90° = 1/0 = Not Defined = ∞
So, for sec, it is
1, 2/√3, √2, 2, ∞
Trigonometry Table - sec sc.jpg
For cot
We know that
cot θ = 1/tan θ
For tan, we know that
0, 1/√3, 1, √3, ∞
So, for cot it will be
cot 0° = 1 / tan 0° = 1/0 = Not Defined = ∞
cot 30° = 1 / tan 30° = 1/(1/√3) = √3
cot 45° = 1 / tan 45° = 1/1 = 1
cot 60° = 1 / tan 60° = 1/√3
cot 90° = 1 / tan 90° = 1/∞ = 0
So, for cot, it is
∞, √3, 1, 1/√3, 0