Key Points - Introduction to Trigonometry

- Trigonometry is the branch of Mathematics which deals with the measurement of sides and angles of the triangles.

- In a right triangle ABC, right-angled at B,

-  sin A =  side opposite to angle A /hypotenuse

cos A = side opposite to angle A / hypotenuse 

s tan A =  side opposite to angle A  / side adjacent to angle A

cos ec A = 1/ sin A; sec A =  1/ cos A
 
tan A = 1 /  cot A

tan A =  sin A / cos A

If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.

- The values of trigonometric ratios for angles 0°, 30°, 45°, 60° and 90°.

- The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.

-  sin (90° – A) = cos A, cos (90° – A) = sin A;

-  tan (90° – A) = cot A, cot (90° – A) = tan A;

-  sec (90° – A) = cosec A, cosec (90° – A) = sec A.

-  sin 2 A + cos2 A = 1,

-  sec2 A – tan2 A = 1 for 0° ≤ A < 90°,

-  cos ec 2 A = 1 + cot2 A for 0° < A ≤ 90º.