Trigonometry Values

If a rotation from the initial position to the terminal position is (`1/360` )^th of the revolution, the angle is said to have a measure of one degree and written as 1°. A degree is divided into minutes, and minute is divided into seconds.

The trigonometric values that exist are based on the angle which are formed of the rotation which represents it provides numeric nalues for the angles in the functions.

Tables for trigonometry values:

The following table in trigonometry shows that the trigonometric radians for their degrees.

The following table in trigonometry shows that the trigonometric functions which provide the trigonometric values for their degrees of their angles.

By the use of this table, the given trigonometric functions with their values  are also used for finding the other trigonometric functions like secant, cosecant and cotangent.

Example problems for trigonometry values:

1.Simplify :

(i) tan 735° (ii) cos 980° (iii) sin 2460° (iv) cos (−870°)
(v) sin (−780°) (vi) cot (−855°) (vii) cosec 2040° (viii)sec (− 1305°)

Solution:
(i) tan (735°) = tan (2 × 360° + 15°) = tan 15°

(ii) cos 980° = cos (2 × 360° + 260°) = cos 260°
= cos (270° - 10°) = − sin 10°

(iii) sin (2460°) = sin (6 × 360° + 300°) = sin (300°)

= sin (360° − 60°)
= − sin 60°
= −`sqrt(3)/2`

(iv) cos (− 870°) = cos (870°) = cos (2 × 360° + 150°)

= cos 150 = cos (180° - 30°)
= − cos 30° = −`sqrt(3)/2`

(v) sin (− 780°) = − sin 780°

= − sin (2 × 360° + 60°)
= − sin 60° = −`sqrt(3)/2`

(vi) cot (− 855°) = − cot (855°) = − cot (2 × 360° + 135°)

= − cot (135°) = − cot (180° - 45°)
= cot 45° = 1

(vii) cosec (2040°) = cosec (5 × 360° + 240°) = cosec (240°)

= cosec (180° + 60°) = − cosec (60°)
= − −`2/3`

(viii) sec (− 1305°) = sec (1305°) = sec (3 × 360° + 225°)

= sec (225°) = sec (270° − 45°)
= − cosec 45° = − 2

2.Simplify :

[  cot (90° − θ ) sin (180° + θ) sec (360° − θ) ] / [ tan (180° + θ) sec (− θ) cos (90° + θ) ]

Solution:

The given expression =[ tan θ (− sin θ) (sec θ) ] / [ tan θ (sec θ) (− sin θ) ]
                                = 1

Because the terms in that fraction gets easily cancelled.