In this article, we shall study to find signs of trigonometric ratios (Functions) in different quadrants formed due to co-ordinate axes. Signs of Trigonometric Ratios in Different Quadrants: θ lies in Quadrant → I II III IV Trigonometric Functions↓ sin θ + ve + ve – ve – ve cos θ + ve – ve […]
In this article, we shall find values of trigonometric ratios of standard angles in the third and the fourth quadrants using a standard unit circle. Trigonometric Ratios of 210o or (7π/6)c: Let us consider a standard unit circle Let m∠ AOP = θ = 210o = (7π/6)c m∠ POM = 30o Ray OA is the initial […]
In this article, we shall find values of trigonometric ratios of standard angles in the first and the second quadrants using a standard unit circle. A circle with the centre at the origin and radius 1 is a standard unit circle. Let P(x, y) be any point on the unit circle with m∠ XOP = […]
Science > Mathematics > Trigonometry > Angle Measurement > Area of Sector In this article, we shall study to solve problems based on the area of the sector. Example – 01: Find the area of a sector of the circle which subtends an angle of 120° at the centre, if the radius of the circle […]
Science > Mathematics > Trigonometry > Angle Measurement > Length of an Arc In this article, we shall solve problems based on the length of an arc (arc length). Example – 01: Find the length of the arc of a circle of diameter 10 cm, if the arc is subtending an angle of 36° at […]
Science > Mathematics > Trigonometry > Angle Measurement > Angle Measurement In this article, we shall study the problems based on the interior angles of a polygon, and the angle between the hour hand and a minute hand of a clock. Example – 01: If xc = 405° and y° = – (π/12)c. Find x […]
In this article, we shall study to find the displacement, velocity, and acceleration of a particle, by the calculus method. Example – 01: A particle is moving in such a way that is displacement ’s’ at any time ‘t’ is given by s = 2t2 + 5t +20. Find the velocity and acceleration of the […]
In this article, we shall study the concept of maximum and minimum values of a function using the concept of differentiation. Example – 01: Find the maximum and minimum values of x3 – 12x – 5 Solution: Let ƒ(x) = x3 – 12x – 5 ………….. (1) Differentiating equation (1) w.r.t. x ƒ’(x) = 3×2 […]
In this article, we shall study more examples to find the equation of normal and tangent to a curve at a given point. Example – 12: Find the equation of the tangent and normal to the curve x = sin θ and y = cos 2θ at θ = π/6 Solution: The equation of the […]
In this article, we shall study the use of the concept of differentiation to find slope, equation of tangent, and normal. Example – 01: Find the equation of the tangent and normal to the curve y = 3×2 – x + 1 at point P(1, 3) Solution: Equation of curve is y = 3×2 – […]