Chapter 8 · Class 10 CBSE · Formula Sheet
Introduction to Trigonometry Formulas — Class 10 CBSE
Define trigonometric ratios, find values of standard angles, and prove trigonometric identities.
Key Formulas
sin
\sin\theta = \dfrac{\text{Opposite}}{\text{Hypotenuse}}
cos
\cos\theta = \dfrac{\text{Adjacent}}{\text{Hypotenuse}}
tan
\tan\theta = \dfrac{\text{Opposite}}{\text{Adjacent}} = \dfrac{\sin\theta}{\cos\theta}
cosec
\csc\theta = \dfrac{1}{\sin\theta}
sec
\sec\theta = \dfrac{1}{\cos\theta}
cot
\cot\theta = \dfrac{1}{\tan\theta} = \dfrac{\cos\theta}{\sin\theta}
Standard Values
\sin 0° = 0, \quad \sin 30° = \dfrac{1}{2}, \quad \sin 45° = \dfrac{\sqrt{2}}{2}, \quad \sin 60° = \dfrac{\sqrt{3}}{2}, \quad \sin 90° = 1
Identity 1
\sin^2\theta + \cos^2\theta = 1
Identity 2
1 + \tan^2\theta = \sec^2\theta
Identity 3
1 + \cot^2\theta = \csc^2\theta
Complementary Angles
\sin(90° - \theta) = \cos\theta, \quad \cos(90° - \theta) = \sin\theta
Worked Examples
1Using: sin 30
Find sin 30 + cos 60.
Step 1: sin 30 = 1/2, cos 60 = 1/2.
Step 2: Sum = 1/2 + 1/2 = 1.
Answer: 1
2Using: tan identity
If tan A = 3/4, find sin A.
Step 1: In right triangle: opposite = 3, adjacent = 4.
Step 2: hypotenuse = 5. sin A = 3/5.
Answer: 3/5
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