trignometry

Key Notes
Chapter-08

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,
side opposite to angle A side opposite to angle A
• sin A = , cos A =
hypotenuse hypotenuse
side opposite to angle A
s tan A =
side adjacent to angle A

1 1
cos ec A = ;sec A =
sin A cos A

1 sin A
tan A = , tan A =
cot 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.




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