Trigonometry Formulas For Class 10

trigonometric ratios :

These tables provide pre-calculated values, making it easier to solve trigonometric equations or perform trigonometric calculations without the need for a calculator.

	0°	30°	45°	60°	90°
sin	0	1/2	√2/2	√3/2	1
cos	1	√3/2	√2/2	1/2	0
tan	0	√3/3	1	√3	undef
cot	∞	√3	1	1/√3	0
csc	∞	2	√2	2/√3	1
sec	1	2/√3	√2	2	undef

trigonometric ratios of complementary angles:

1. Sine:
   Sin(A) = cos(90° – A)
2. Cosine:
   Cos(A) = sin(90° – A)
3. Tangent:
   Tan(A) = cot(90° – A)
4. Cotangent:
   Cot(A) = tan(90° – A)
5. Secant:
   Sec(A) = csc(90° – A)
6. Cosecant:
   Csc(A) = sec(90° – A)

These formulas allow you to find the trigonometric ratio of an angle’s complementary angle without directly calculating the complementary angle.

Pythagorean Identities:

sin²(A) + cos²(A) = 1
1 + tan²(A) = sec²(A)
1 + cot²(A) = csc²(A)
Reciprocal Identities:

csc(A) = 1 / sin(A)
sec(A) = 1 / cos(A)
cot(A) = 1 / tan(A)

These identities are used extensively in trigonometry to simplify expressions, solve equations, and prove various trigonometric relationships. They form the foundation for many other trigonometric identities and are essential for understanding the behavior of trigonometric functions.

Trigonometric ratio:

1. Sine (sin):
   sin(A) = opposite/hypotenuse
2. Cosine (cos):
   cos(A) = adjacent/hypotenuse
3. Tangent (tan):
   tan(A) = opposite/adjacent
4. Cosecant (csc):
   csc(A) = 1/sin(A)
5. Secant (sec):
   sec(A) = 1/cos(A)
6. Cotangent (cot):
   cot(A) = 1/tan(A)

These formulas represent the ratios between the sides of a right triangle and are commonly used in trigonometry to calculate unknown angles or side lengths.