Sin Cos Tan Values: Overview, Questions, Preparation

We study different sides and angles of a right-angled triangle in trigonometry. Trigonometry has some primary functions that are sine, cosine, and tangent.

Below mentioned are some of the important trigonometric functions:

While finding the sin, cos, and tan values of a triangle, 00, 300, 450, 600, and 900 angles are considered. The formulas for calculating sin, cos, and tan values are as follows:

• Sin Ɵ = Opposite Side / Hypotenuse = BC / AC
• Cos Ɵ = Adjacent Side / Hypotenuse = AB / AC
• Tan Ɵ = Opposite Side / Adjacent Side = BC / AB

Thus, tan Ɵ = sin Ɵ / cos Ɵ

Sin Cos Tan Chart

Sin, cos and tan functions are considered as primary functions for solving various trigonometric problems. Trigonometry is an important section of mathematics for the students of class X. This section carries a weightage of around 6 marks in the examination. 

sin 00 = √(0/4) = 0

sin 300 = √(1/4) = 1/2

sin 450 = √(2/4) = 1/√2

sin 600 = √3/4 = √3/2

sin 900 = √(4/4) = 1

cos 00 = √(4/4) = 1

cos 300 = √(3/4) = √3/2

cos 450 = √(2/4) = 1/√2

cos 600 = √(1/4) = 1/2

cos 900 = √(0/4) = 0

tan 00 = 0/1 = 0

tan 300 = [(√1/4) / (√3/4)] = 1/√3

tan 450 = √(2/4) = 1/√2

tan 600 = [(√3/2) / (1/2)] = √3

tan 900 = 1/0 = ∞

Example 1. A wire of radius 3 cm is bent and cut so that it can lie along the circumference of a hoop which is around 48 cm. Calculate the angle which is subtended at the centre of the hoop. 

Solution: 

Length = 2π x 3 = 6π cm

Here, s = 6π cm (length of the arc) and r = 48 cm (radius of the circle)

Thus, Ө = Arc/Radius = 6π/48 = π/8 = 22.50

Example 2. If A = cos2Ө + sin4Ө for all the values of Ө, then prove 3/4 ≤ A ≤1

Solution:

A = cos2Ө + sin4Ө = cos2Ө + sin2Ө sin2Ө ≤ cos2Ө + sin2Ө

Thus, A ≤ 1

Also, A = cos2Ө + sin4Ө = ( 1 - sin2Ө) + sin4Ө 

= (sin2Ө - 1/2)2 + (1 - 1/4) = (sin2Ө - 1/2)2 + 3/4 ≥ ¾

Thus, 3/4 ≤ A ≤ 1

 Example 3. If tan Ө = -4/3, then sinӨ is

1. -4/5 but not 4/5 
2. -4/5 or 4/5
3. 4/5 but not -4/5 
4. None of the above

Solution:

As tan Ө = -4/3 is negative, Ө lies either in third or the fourth quadrant. Thus, sin Ө = 4/5 if the Ө lies in the second quadrant and sin Ө = -4/5  if the Ө lies in the fourth quadrant. Thus, the correct answer would be option 2.

Q: State the primary function of trigonometry?

Q: Where is trigonometry applied in real-life?

Q: Who has founded trigonometry?

Q: Which are the basic trigonometric functions?

Q: What are the applications of trigonometry?