IBDP Mathematics: Functions and Trigonometry

In IB Mathematics, there are trigonometric identities as follows.

• sec x = 1/cos x
• cosec x = 1/sin x
• cot x = 1/tan x
• tanθ = sinθ/ cosθ
• cos²θ + sin²θ = 1
• 1 + tan²θ = sec²θ
• cot²θ + 1 = cosec²θ

Note: When asked to show by counter-example that a statement is false, sub a value in and show that LHS is not equal to RHS.

Sin (A + B) = sin A cos B + cos A sin B

Sin (A - B) = sin A cos B - cos A sin B

Cos (A + B) = cos A cos B - sin A sin B

Cos (A - B) = cos A cos B + sin A sin B

When it comes to IB Mathematics, the transformations so far follow these rules:

• f(x) + a is f(x) shifted upward a units
• f(x) – a is f(x) shifted downward a units
• f(x + a) is f(x) shifted left a units
• f(x – a) is f(x) shifted right a units
• –f(x) is f(x) flipped upside down ("reflected about the x-axis")
• f(–x) is the mirror of f(x) ("reflected about the y-axis")

This is the end of this topic.

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