Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Trigonometric terms in a geometric progression

Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.

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Recall · M4U-P1-QP-SERIES-TRIG-GEOMETRIC-01

angles in GP

Maths4U Original · Short practice

Angles \(10^\circ,30^\circ,\theta\) are consecutive GP terms. Find \(\theta\) in degrees.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Method · M4U-P1-QP-SERIES-TRIG-GEOMETRIC-02

GP trig constraint

Maths4U Original · Short practice

\(\cos60^\circ,k,\cos0^\circ\) form a GP with \(k>0\). Find \(k^2\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Apply · M4U-P1-QP-SERIES-TRIG-GEOMETRIC-03

trig ratio sum

Maths4U Original · Short practice

A GP has first term \(\sin30^\circ\) and ratio \(\cos60^\circ\). Find its sum to infinity.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Check understanding · M4U-P1-QP-SERIES-TRIG-GEOMETRIC-04

angle convergence restriction

Maths4U Original · Short practice

A geometric series has a nonzero first term and common ratio \(\tan\theta\), where \(0<\theta<\pi/2\). For which values of \(\theta\) does the series converge?

Choose one answer.

Fresh review variant · M4U-P1-QP-VAR-SERIES-TRIG-GEOMETRIC-01

angles in GP

Maths4U Original · Short practice

The angles \(5^\circ,20^\circ,\theta\) are consecutive GP terms. Find theta in degrees.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-SERIES-TRIG-GEOMETRIC-02

GP trig constraint

Maths4U Original · Short practice

\(\cos60^\circ,k,\sin30^\circ\) are consecutive GP terms with k positive. Find \(k^2\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-SERIES-TRIG-GEOMETRIC-03

trig ratio sum

Maths4U Original · Short practice

A GP has first term \(\sin90^\circ\) and ratio \(\cos60^\circ\). Find its infinite sum.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-SERIES-TRIG-GEOMETRIC-04

angle convergence restriction

Maths4U Original · Short practice

For \(0<\theta<90^\circ\), a GP ratio is \(\tan\theta\). The convergence condition is \(\thetaEnter one number or fraction. Round decimals to at least six decimal places when needed.