The Trigonometric Functions (HSC SSCE Mathematics Advanced): Quizzes

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The Behaviour of sin x Near the Origin
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What is the gradient of y=sin⁡xy = \sin x as it passes through the origin?

11

For acute angles xx, which inequality is correct?

sin⁡x<x<tan⁡x\sin x < x < \tan x

For −π2<x<0-\frac{\pi}{2} < x < 0, which inequality is correct?

sin⁡x>x>tan⁡x\sin x > x > \tan x

What is lim⁡x→0sin⁡xx\lim_{x \to 0} \frac{\sin x}{x}?

11

Which line is tangent to both y=sin⁡xy = \sin x and y=tan⁡xy = \tan x at the origin?

y=xy = x

For small angles in radians, sin⁡x\sin x is approximately equal to what?

xx

For small angles in radians, cos⁡x\cos x is approximately equal to what?

11

In which unit must angles be expressed for small-angle approximations to work?

Radians

In the geometric proof, which areas are compared?

Two triangles and a sector

What is lim⁡x→0tan⁡xx\lim_{x \to 0} \frac{\tan x}{x}?

11

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

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Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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