What are the 12 trigonometric identities?
Sum and Difference of Angles Trigonometric Identities
- sin(α+β)=sin(α).cos(β)+cos(α).sin(β)
- sin(α–β)=sinα.cosβ–cosα.sinβ
- cos(α+β)=cosα.cosβ–sinα.sinβ
- cos(α–β)=cosα.cosβ+sinα.sinβ
- tan. ( α + β ) = tan β 1 – tan α . tan. β
- tan. ( α – β ) = tan β 1 + tan α . tan.
How do you find tan 120 degrees?
For tan 120 degrees, the angle 120° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 120° value = -√3 or -1.7320508. . . Since the tangent function is a periodic function, we can represent tan 120° as, tan 120 degrees = tan(120° + n × 180°), n ∈ Z.
What is the formula of tan 30?
Tan 30 degree is equal to 1/√3 and its exact value is 0.57735.
How do you solve COS 135 degrees?
The value of cos 135 degrees can be calculated by constructing an angle of 135° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of cos 135° is equal to the x-coordinate (-0.7071). ∴ cos 135° = -0.7071.
What are the 6 formulas of trigonometry?
Trigonometric Ratios
- The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
- sin C = (Side opposite to ∠C)/(Hypotenuse) = AB/AC.
- cos C = (Side adjacent to ∠C)/(Hypotenuse) = BC/AC.
What is the value of tangent θ?
Values of Trigonometric Ratios
| Angles | 0∘ | 90∘ |
|---|---|---|
| Tan θ | 0 | ∞ |
| Cot θ | ∞ | 0 |
| Sec θ | 1 | ∞ |
| Cosec θ | ∞ | 1 |
What is sin 120 degree value?
Therefore, sin 120° = √3/2.
What is the value of Sinπ?
= 0
What is the value of sin pi? In trigonometry, we use pi (π) for 180 degrees to represent the angle in radians. Hence, sin π is equal to sin 180 or sin π = 0.
What is the tan of 45?
1
The exact value of tan 45 degrees is 1.
What is the value tan 60?
√3
Therefore, the exact value of tan 60 degrees is √3.
What is COS 135 in radians?
Trigonometric Function Values of Special Angles
| θ° | θradians | cos(θ) |
|---|---|---|
| 120° | 2π/3 | -1/2 |
| 135° | 3π/4 | -√2/2 |
| 150° | 5π/6 | -√3/2 |
| 180° | π | -1 |
How do you solve sin 135 degrees?
The value of sin 135 degrees can be calculated by constructing an angle of 135° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of sin 135° is equal to the y-coordinate (0.7071). ∴ sin 135° = 0.7071.
What are the 4 types of trigonometry?
There are four types of trigonometry used today, which include core, plane, spherical and analytic. Core trigonometry deals with the ratio between the sides of a right triangle and its angles.
What is the ratio of sine θ?
| Trigonometric Ratios | |
|---|---|
| Sin θ | Opposite Side to θ/Hypotenuse |
| Tan θ | Opposite Side/Adjacent Side & Sin θ/Cos θ |
| Cot θ | Adjacent Side/Opposite Side & 1/tan θ |
| Sec θ | Hypotenuse/Adjacent Side & 1/cos θ |
What is the value of sin ∅?
Sine is one of the primary trigonometric functions which helps in determining the angle or sides of a right-angled triangle. It is also called trigonometric ratio. If theta is an angle, then sine theta is equal to the ratio of perpendicular and hypotenuse of the right triangle. To be noted the value of sin 0 is also 0.
What is the value of cos ∅?
The value of cos 0 is 1. Here, we will discuss the value for cos 0 degrees and how the values are derived using the quadrants of a unit circle. The trigonometric functions are also known as an angle function that relates the angles of a triangle to the length of the triangle sides.
What is the cot of 120?
-0.5774
Cot 120 degrees is the value of cotangent trigonometric function for an angle equal to 120 degrees. The value of cot 120° is -(1/√3) or -0.5774 (approx).
What is COS 120 in radians?
-0.5
The value of cos 120 degrees is -0.5. Cos 120 degrees in radians is written as cos (120° × π/180°), i.e., cos (2π/3) or cos (2.094395. . .).
What is the value of sin270?
-1
Answer: Sin 270 degrees has a value of -1.
How do you find sin270?
The value of sin 270 degrees is -1.
…
We can use trigonometric identities to represent sin 270° as,
- sin(180° – 270°) = sin(-90°)
- -sin(180° + 270°) = -sin 450°
- cos(90° – 270°) = cos(-180°)
- -cos(90° + 270°) = -cos 360°
What is the sin and cos of 45?
The exact value of sin(45°) sin ( 45 ° ) is √22 . The exact value of cos(45°) cos ( 45 ° ) is √22 .
Why is tan 60?
For tan 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 60° value = √3 or 1.7320508. . . Since the tangent function is a periodic function, we can represent tan 60° as, tan 60 degrees = tan(60° + n × 180°), n ∈ Z.
What is the exact value of cosine 135?
Answer and Explanation: The exact value of cos(135°) is -√(2) / 2.
What is the reference angle of COS 135?
135′ is in the second quadrant, so our reference angle is 180′-135 “, or 45′ .
What is the value of sin 135 )?
0.7071
Sin 135 degrees is the value of sine trigonometric function for an angle equal to 135 degrees. The value of sin 135° is 1/√2 or 0.7071 (approx).