Class 10 Mathematics, Chapter 8, Introduction to Trigonometry
1. What is Trigonometry?It’s basically just calculating the sides and angles of a right-angled triangle. The three sides of the triangle are: Hypotenuse ($H$): The longest side (opposite the 90° angle). Perpendicular ($P$): The side standing opposite to the angle ($theta$) you're looking at. Base ($B$): The bottom side next to angle $theta$. 2. The Core FormulasThese are the main formulas to remember: $sintheta = frac{text{Perpendicular}}{text{Hypotenuse}}$ $costheta = frac{text{Base}}{text{Hypotenuse}}$ $tantheta = frac{text{Perpendicular}}{text{Base}}$ And these three are just the flipped versions: $text{cosec}theta = frac{text{Hypotenuse}}{text{Perpendicular}}$ $sectheta = frac{text{Hypotenuse}}{text{Base}}$ $cottheta = frac{text{Base}}{text{Perpendicular}}$ 3. Angle Values TableAngle (θ)sincostancosecseccot$0^circ$$0$ $1$ $0$ — $1$ — $30^circ$$frac{1}{2}$ $frac{sqrt{3}}{2}$ $frac{1}{sqrt{3}}$ $2$ $frac{2sqrt{3}}{3}$ $sqrt{3}$ $45^circ$$frac{sqrt{2}}{2}$ $frac{sqrt{2}}{2}$ $1$ $sqrt{2}$ $sqrt{2}$ $1$ $60^circ$$frac{sqrt{3}}{2}$ $frac{1}{2}$ $sqrt{3}$ $frac{2sqrt{3}}{3}$ $2$ $frac{1}{sqrt{3}}$ $90^circ$$1$ $0$ — $1$ — $0$ 4. Important Rules (Identities)Keep these three rules handy for solving big equations:$sin^2theta + cos^2theta = 1$ $1 + tan^2theta = sec^2theta$ $1 + cot^2theta = text{cosec}^2theta$ 5. Complementary Angles ($90^circ - theta$)When two angles add up to 90°, they swap roles like this: $sin(90^circ - theta) = costheta$ $cos(90^circ - theta) = sintheta$ $tan(90^circ - theta) = cottheta$
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