Trigonometry
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Trigonometry Table:
| Angle | 0° | 30° | 45° | 60° | 90° |
| Sinθ | 0 | $$\frac{1}{2}$$ | 1/√2 | √3/2 | 1 |
| Cosθ | 1 | √3/2 | 1/√2 | ½ | 0 |
| Tanθ | 0 | 1/√3 | 1 | √3 | Undefined |
| Cotθ | Undefined | √3 | 1 | 1/√3 | 0 |
| Secθ | 1 | 2/√3 | √2 | 2 | Undefined |
| Cosecθ | Undefined | 2 | √2 | 2/√3 | 1 |
Trigonometric formulas:
- sin(90° – θ) = cos θ
- cos(90° – θ) = sin θ
- tan(90° – θ) = cot θ
- cot(90° – θ) = tan θ
- sec(90° – θ) = cosecθ
- cosec(90° – θ) = secθ
- sin2θ + cos2 θ = 1
- sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
- Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Trigonometric Formula
| \(\sin (-\theta ) = -\sin \theta\) | \(\cos (-\theta ) = \cos \theta\) |
| \(\tan (-\theta ) = -\tan \theta\) | \(\cot (-\theta ) = -\cot \theta\) |
| \(\sec (-\theta ) = \sec \theta\) | \( cosec (-\theta ) = -cosec \theta\) |
| \(\sin \, A \,\ sin \, B = \frac{1}{2}\left [ \cos\left ( A – B \right ) -\cos \left ( A+B \right ) \right ]\) | |
| \(\cos\, A \, \cos\, B = \frac{1}{2}\left [ \cos \left ( A – B \right ) + \cos \left ( A+B \right ) \right ]\) | |
| \(\sin\, A \, \cos\, B = \frac{1}{2}\left [ \sin\left ( A + B \right ) + \sin \left ( A-B \right ) \right ]\) | |
| \( \cos\, A \, \sin\, B = \frac{1}{2}\left [ \sin\left ( A + B \right ) – \sin\left ( A-B \right ) \right ]\) |
2 If cos20° = m and cos70° =n, then the value of m2 + n2 is?
A
$$\frac{1}{2}$$
B
1
C
$$\frac{3}{2}$$
D
$$\frac{1}{{\sqrt 2 }}$$
3 If (1 + cosA)/(1 - cosA) = x, then x is
A
cot2A/(secA - 1)2
B
cot2A/(secA + 1)2
C
tan2A/(secA + 1)2
D
tan2A/(secA - 1)2
7 If sinC - sinD = x, then value of x is
A
2sin[(C+D)/2]cos[(C-D)/2]
B
2cos[(C+D)/2]cos[(C-D)/2]
C
2cos[(C+D)/2]sin[(C-D)/2]
D
2sin[(C+D)/2]sin[(D-C)/2]
