Trigonometry Formulas class-10

 Consider a right-angled triangle have angle ∠θ, then

sin θ= Perpendicular / Hypotenuse = P/H

Cos θ=Base / Hypotenuse = B/H

Tan θ= Perpendicular / Base = P / B

Cosec θ=1/sin θ

Sec θ=1/cosθ

Cot θ=1/tan θ

Tan θ=Sin θ / Cos θ

$\begin{array}{l}\mathrm{sin\; \theta =\; Perpendicular\; /\; Hypotenuse\; =\; P/H}\end{array}$$\begin{array}{l}\mathrm{Cos\; \theta =Base\; /\; Hypotenuse\; =\; B/H}\end{array}$$\begin{array}{l}\mathrm{Tan\; \theta =\; Perpendicular\; /\; Base\; =\; P\; /\; B}\end{array}$$\begin{array}{l}\mathrm{Cosec\; \theta =1/sin\theta }\end{array}$$\begin{array}{l}\mathrm{Sec\; \theta =1/cos\theta }\end{array}$$\begin{array}{l}\mathrm{Cot\; \theta =1/tan\theta }\end{array}$$\begin{array}{l}\mathrm{Tan\; \theta =Sin\; \theta \; /\; Cos\; \theta }\end{array}$$\begin{array}{l}\mathrm{ C}ot\frac{\mathrm{<o:p></o:p>}}{}\end{array}$

$\begin{array}{l}Tan\theta =\frac{Sin\theta }{\mathrm{/\; C}os\mathrm{\theta <o:p></o:p>}}\end{array}$

Trigonometry Table:

Angle	0°	30°	45°	60°	90°
Sinθ	0	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

 

• 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°