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# Tangent

## 1.2 Derivatives Basic Concepts – Tangent and Derivatives

#### Chord, Secant, and Tangent

• A chord is a line segment joining two points on a curve, like the line AB in the previous example.
• A secant is a line that passes through two points, which means that it can be longer than a chord for any given two points A and B.
• Graphically, ‘a tangent though a curve at point P’ is defined as a line that passes through P and its gradient equals the curve’s instantaneous rate of change at P.
• Suppose P has coordinates P(p,\:f(p)), then \text {Gradient of tangent at } P=\lim _{h \rightarrow 0} \frac{f(p+h)-f(p)}{h}

Note: Here, h \rightarrow 0 is used and not h \rightarrow 0^{+}.

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## 5.3 Solution of Trigonometric Equations

#### Basic Trigonometric Equations (Sine and Cosine)

• The most basic equations in polynomials would be linear equations, such as ax+b=c (which gives you x=\frac{c-b}{a}). The trigonometric equivalent ones would be \sin t =a or \cos t =b, and you are supposed to solve for t.
• Be careful, as solving trigonometric equations are not as simple. Refer to the examples below.
• For each such equations, unless a restriction on x (or more commonly used in trigonometric, \theta), there will be infinite or no solutions for x. This is because of the periodic and symmetric properties that they have.
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## 1.5 Trigonometric Functions Background Knowledge

• The term ‘radian’ actually originated when we wanted to find a neat expression for the angle when the corresponding arc length of a circle with 1 unit radius, for this angle, is also 1 unit. Using degrees, the number will not look nice, hence a new unit called radians are invented.