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Updated on 22nd July, 2024 , 4 min read
The fundamental trigonometric ratios of sin, cos, and tan are used to study the relationship between the angles and sides of a triangle, particularly a right-angled triangle. Hipparchus used the principles of trigonometry to establish the relationship between the sides and angles of a right triangle, whereas Pythagoras focused on the relationship between a right triangle's sides through the Pythagorean theorem. A right-angled triangle's missing sides or angles can be found using the trigonometry formulas sin, cos, and tan.
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The three fundamental trigonometric ratios, namely sine, cosine, and tangent, each give the ratio of the lengths of the two sides of a right-angled triangle. We are aware that the three sides of a right-angled triangle are called the "legs" and the "hypotenuse," respectively. Thus, the longest side of a right-angled triangle is still referred to as the "hypotenuse" in trigonometry, while the other two legs are given the names:
Based on the angle we are discussing, we determine the "opposite" and "adjacent" sides.
The values of the trigonometric functions are tabulated below.
Angles (in degrees) | 0° | 30° | 45° | 60° | 90° |
Angles (in radian) | 0 | π/6 | π/4 | π/3 | π/2 |
Sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
Cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
Tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
Cot θ | ∞ | √3 | 1 | 1/√3 | 0 |
Sec θ | 1 | 2/√3 | √2 | 2 | ∞ |
Cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |
The things that you need to keep in mind from this chart are:
The trigonometric ratios sin, cos, and tan are frequently used in everyday life to calculate heights and distances. Sin, cos, and tan are used to solve a variety of real-world issues. Even the motions and distances of planets are calculated using it.
The steps listed below can help you remember the trigonometric values provided in the above table:
Hence, the sin cos tan values are found.
A cosecant function is the sine function's reciprocal function, and vice versa. Similarly, the secant function is the cosine function's reciprocal function, and the cotangent function is the tangent function's reciprocal function.
The Pythagorean identities of trigonometric functions are as follows:
The negative angle of a cosine function is always equal to the angle's positive cosine, whereas the negative angle of a sine and tangent function is equal to the angle's negative sine and tangent.
Answer:
We can deduce from the trigonometric identities that sin2
sin2 30o + cos230o = (½)2 + (√3/2)2 = ¼ + ¾
= 4/4
=> 1
Answer:
It is understood that sin θ is positive and tan θ is negative. So θ must be in Quadrant II, where cos θ is negative. Now, sin θ = 2/3 = Opposite/Hypotenuse.
So we can assume that Opposite = 2k, Hypotenuse = 3k.
By Pythagoras theorem,
Adjacent2 = Hypotenuse2 - Opposite2
⇒ (3k)2 - (2k)2 = 5k2
Adjacent = √5k
Hence, Cos θ = - Adjacent/Hypotenuse = -√5k/3k = -√5/3
Answer:
We all know that through trigonometric table that sin 60°= ½, cos 30°= √3/2 sin 30° = √3/2, cos 60°= ½
So, putting the values in the question, we get
½+√3/2 + √3/2+½
= 2+2√3/2
The following formulas are used to determine sin, cos, and tan: 1. sin θ = Opposite/Hypotenuse 2. cos θ = Adjacent/Hypotenuse 3. tan θ = Opposite/Adjacent
Because the value is too large to be assigned a specific value, the value of tan 90° is not defined in a trigonometry table.
In a sin, cos, tan table, the angles 0°, 30°, 45°, 60°, and 90° are referred to as "standard angles" because we frequently use their trigonometric values to solve trigonometry problems.
The value of Sin 0° is 0.
SOH CAH TOA is a mnemonic that helps us remember the three major trigonometric ratios. They are known as sine (sin), cosine (cos), and tangent (tan).
The trigonometric functions sine, cosine, and tangent are abbreviated as sin, cos, and tan.
Hipparchus is known as the king of trigonometry. He was a Greek astronomer, geographer, and mathematician.
Trigonometry uses sin, cos, and tan to calculate the values of these functions while establishing a relationship between the angles and sides of a triangle (especially a right-angled triangle).
The basic trigonometric ratios in trigonometry are sin, cos, and tan, which are used to study the relationship between the angles and sides of a triangle (especially a right-angled triangle).