Trigonometric terms in a geometric progression: check 1
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: check 2
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: check 3
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
A geometric series has a nonzero first term and common ratio \(\tan\theta\), where \(\displaystyle 0< \theta < \frac{\pi }{2}\). For which values of \(\theta\) does the series converge?Choose one answer.
Trigonometric terms in a geometric progression: review variant 1
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: review variant 2
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: review variant 3
Difficulty: ★★☆Info
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.
Trigonometric terms in a geometric progression: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(0<\theta<90^\circ\), a GP ratio is \(\tan\theta\). The convergence condition is \(\theta<a^\circ\). Find a.Enter one number or fraction. Round decimals to at least six decimal places when needed.