11th Physics Basics
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– Quadratic Formula: \(x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\) – Used to find the roots of a quadratic equation \(ax^2 + bx + c = 0\)【4:3†source】.
– Trigonometric Functions of Angle \(\theta\): \(\sin \theta = \frac{y}{r}\), \(\cos \theta = \frac{x}{r}\), \(\tan \theta = \frac{y}{x}\), \(\cot \theta = \frac{x}{y}\), \(\sec \theta = \frac{r}{x}\), \(\csc \theta = \frac{r}{y}\) – Relationships between trigonometric functions in a right triangle with angle \(\theta\)【4:3†source】.
– Pythagorean Theorem: In a right triangle, \(a^2 + b^2 = c^2\) where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse【4:3†source】.
– Trigonometric Identities: Various trigonometric identities and formulas including sine, cosine, tangent sum and difference formulas, exponential expansion, logarithmic expansion, and the binomial theorem【4:3†source】.
What is the formula for the area of a triangle in terms of its base and altitude?
The formula for the area of a triangle is 1/2 * base * altitude.
State the Pythagorean theorem in the context of a right triangle.
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), expressed as c^2 = a^2 + b^2.
What does the trigonometric identity sin(90° – θ) equal to?
The trigonometric identity sin(90° – θ) is equal to cos θ.
Explain the relationship between sec^2 θ, tan^2 θ, and 1 in trigonometry.
The relationship between sec^2 θ, tan^2 θ, and 1 in trigonometry is sec^2 θ – tan^2 θ = 1.
What is the formula for calculating the volume of a right circular cylinder?
The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius and h is the height of the cylinder.
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