STD IX – TRIGONOMETRY – ARCHIMEDES

TRIGONOMETRICAL RATIOS

Each trigonometric ratio is a real number and has no unit.

The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle if the angle remains the same.

Since the hypotenuse is the longest side in a right triangle, the value of sin A or cos A is always less than 1 (or, in particular, equal to 1).

TRIGONOMETRICAL RATIOS OF STANDARD ANGLES

Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. The standard angles for these trigonometric ratios are 0°, 30°, 45°, 60° and 90°. These angles can also be represented in the form of radians such as 0, π/6, π/4, π/3, and π/2.

SOLUTION TO RIGHT TRIANGLES

Learn how to solve right triangles. In this course we will talk about finding all the side lengths and angles in a right triangle.  We will use right triangle trigonometry, inverse trig functions, as well as Pythagorean theorem.

Trigonometric ratios of complementary angles

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

COMPLEMENTARY ANGLES

Complementary angles are angle pairs whose measures sum to one right angle (1/4 turn, 90°, or π/2 radians).

If the two complementary angles are adjacent their non-shared sides form a right angle. The difference between an angle and a right angle is termed the complement of the angle.