cosine formula cosine rule

If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that a 2 = b 2 + c 2 - 2 bc cos A, b 2 = c 2 + a 2 - 2 ca cos B, c 2 = a 2 + b 2 - 2 ab cos ..

The Indian mathematician Aryabhata, gave tables of half chords which are now known as sine tables, along with cosine tables. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light wave..

A part of the natural cosine tables is given below: Find from the tables the value of (i) cos 37 o (ii) cos 37 o 42 ' (iii) cos 37 o 45 ' (i) cos 37 o Find 37 o on the 'Natural Cosines' table in 'A' group. As there are no minutes, the value is read horizontally under the 0 ' col..

Cosine is represented as => Hypotenuse/ Opposite side or Hypotenuse/ Adjacent side or Adjacent side/ Hypotenuse or Opposite side/ Adjacent side..

Identify the cosine function from the graphs. => Graph 4 or Graph 5 or Graph 1 or Graph 3 or Graph 2..

A surveyor obtains an angle of 33° 49′ between two merging roads. Find the cosine of that angle. => 0.8308 or 1.7968 or -1.3552 or -0.4823..

Find exact value of the cosine of the angle 225° by using a right triangle. => 1 2 or 2 2 or - 1 2 or - 2 2..

A cosine graph with amplitude 4 and period 180° is translated 1 unit down. Identify the equation of the graph after transformation. => y = 4cos 2 θ + 3 or y = 4cos 2 θ - 1 or y = 2cos 4 θ - 1 or y = 4cos 2 θ + 1..

A cosine graph with amplitude 6 and period 45° is translated 1 units down. Identify the equation of the graph after transformation. => y = 6cos 8 θ - 1 or y = 6cos 8 θ + 1 or y = 6cos 3 θ + 1 or y = 6cos 3 θ - 1..

Identify the equation for a cosine function of peroid 45° , after a phase shift 60° to the left. => y = cos [8( θ + 60°)] or y = cos [3( θ - 60°)] or y = cos [3( θ + 60°)] or y = cos [8( θ - 60°)]..