Mathematics can be a really hard subject for students to understand. There are many concepts in maths that can be challenging as well so, we will talk about one of those challenging concepts today; Trigonometric values. The primary ones are Sin θ, Cos θ, and Tan θ. We also will discuss Cosec θ, Sec θ and Cot θ. While calculating these values, the
angles that we take are 0°. 30°, 45°, 60°, and 90°. If you feel confused and have no idea about the value of sin 30°, cos 90°, tan 45° and cosec 0° then you are on the right track.
First, we need to know about how these values relate to each other. For that we should know these points:
- Tan θ = sin θ/cos θ
- Cot θ = 1/ tan θ = cos θ/sin θ
- Sin θ = 1/cosec θ = tan θ/sec θ
- Cos θ = 1/ sec θ= sin θ/ tan θ
- Sec θ = 1/cos θ = tan θ/sin θ
- Cosec θ = 1/sin θ = sec θ/tan θ
Sin and Cos are opposite to each other in respective angles.
VALUES OF SIN θ AT DIFFERENT ANGLES:
We are going to list down the values of sin at different angles.
- Sin 0° = 0
- Sin 30° = 12
- Sin 45° = 12
- Sin 60° = 32
- Sin 90° = 1
The values of Sin θ at different angles respectively is mentioned below:
Angles
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Since, sin and cos are opposite to each other so their values would be opposite to each other. To explain this we will list down the values of cos.
VALUES OF COS θ AT DIFFERENT ANGLES:
The value of cos θ are as following:
- Cos 0° = Sin 90° = 1
- Cos 30° = Sin 60° = 32
- Cos 45° = Sin 45° = 12
- Cos 60° = Sin 30° =12
- Cos 90° = Sin 0° = 0
The values of Cos θ at different angles respectively is mentioned below:
Angles
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Cos θ
| 1
| 32
| 12
| 12
| 0
|
As we all know that Tan θ = sin θ/cos θ, so we can figure out that the values would relate to each other through the formula. To show this, we are going to list down the values of Tan θ.
VALUES OF TAN θ AT DIFFERENT ANGLES:
The value of tan θ are as following:
- Tan 0° = Sin 0°/ Cos 0° = 0/1 = 0
- Tan 30° = Sin 30°/ Cos 30° = 12/32 = 13
- Tan 45° = Sin 45°/ Cos 45° = 12/12= 1
- Tan 60° = Sin 60°/ Cos 60° = 32/12= 3
- Tan 90° = Sin 90°/ Cos 90°= 1 / 0 = Not Defined = ∞
The values of Tan θ at different angles respectively is mentioned below:
Angles
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Cos θ
| 1
| 32
| 12
| 12
| 0
|
Tan θ
| 0
| 12
| 1 | 3
| Not Defined ∞
|
Now, we know the values of Sin θ, Cos θ, and Tan θ for different angles respectively. Since, we already are familiar with the formulas to find the other three values that are Cosec θ, Sec θ, and Cot θ, it would be easier to write down their values. Let’s start with the Cosec θ as according to the formula if we divide 1 by the value of Sin θ, we will have the values of Cosec θ at particular angles.
VALUES OF COSEC θ AT DIFFERENT ANGLES:
We are going to list down the values of Cosec θ at different angles. As we know that
Cosec θ = 1/sin θ
- Cosec 0° = 1/ Sin 0° = 1 / 0 = Not Defined = ∞
- Cosec 30° = 1/ Sin 30° = 1 /12= 2
- Cosec 45° = 1/ Sin 45° = 1 / 12= 2
- Cosec 60° = 1/ Sin 60° = 1 /32= 23
- Cosec 90° = 1/ Sin 90° = 1 / 1 = 1
The values of Cosec θ at different angles respectively is mentioned below:
Angles
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Cos θ
| 1
| 32
| 12
| 12
| 0
|
Tan θ
| 0
| 12
| 1
| 3
| Not Defined ∞
|
Cosec θ
| Not Defined ∞
| 2
| 2
| 23
| 1
|
VALUES OF SEC θ AT DIFFERENT ANGLES:
We are going to list down the values of Sec θ at different angles. As we know that
Sec θ = 1/cosec θ
Sec 0° = 1/ Cos 0° = 1 / 1 = 1
Sec 30° = 1/ Cos 30° = 1 /32= 23
Sec 45° = 1/ Cos 45° = 1 / 12= 2
Sec 60° = 1/ Cos 60° = 1 /12= 2
Sec 90° = 1/ Cos 90° = 1 / 0 = Not Defined = ∞
The values of Sec θ is mentioned below in the table:
Angles
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Cos θ
| 1
| 32
| 12
| 12
| 0
|
Tan θ
| 0
| 12
| 1
| 3
| Not Defined ∞
|
Cosec θ
| Not Defined ∞
| 2
| 2
| 23
| 1
|
Sec θ
| 1
| 23
| 2
| 2
| Not Defined ∞
|
VALUES OF COT θ AT DIFFERENT ANGLES:
We are going to list down the values of Cot θ at different angles.
As we know that Cot θ = 1/ tan θ
- Cot 0° = 1/ Tan 0° = 1 / 0 = Not Defined = ∞
- Cot 30° = 1/ Tan 30° = 1 /13= 3
- Cot 45° = 1/ Tan 45° = 1 / 1 = 1
- Cot 60° = 1/ Tan 60° = 1 /3= 13
- Cot 90° = 1/ Tan 90° = 1 / Not Defined (∞) = 0
Since, we have all the values with respectively desired angles we can write them all down in the table.
Angles (Degrees)
| 0°
| 30°
| 45°
| 60°
| 90°
|
Sin θ
| 0
| 12
| 12
| 32
| 1
|
Cos θ
| 1
| 32
| 12
| 12
| 0
|
Tan θ
| 0
| 13
| 1
| 3
| Not Defined ∞
|
Cosec θ
| Not Defined ∞
| 2
| 2
| 23
| 1
|
Sec θ
| 1
| 23
| 2
| 2
| Not Defined ∞
|
Cot θ
| ∞
| 3
| 1
| 13
| 0
|
Since all the values are mentioned in the box and have been solved using the simple formulas discussed above, it would be easier to understand now. Moreover, these values are for significant angles in degrees;however, if they were in radian, the values would have been definitely different. One can learn these values by practicing several times and by just knowing the formula, one can answer all sorts of questions related to these trigonometric values.
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