R sin(x+α) and extrema: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(7 \sin{\left(x \right)} + 24 \cos{\left(x \right)} + 22\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=22\).
Find R.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(24 \sin{\left(x \right)} + 10 \cos{\left(x \right)} + 23\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=23\).
Find R.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(24 \sin{\left(x \right)} + 10 \cos{\left(x \right)} + 23\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=23\).
Find sin α.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(32 \sin{\left(x \right)} + 24 \cos{\left(x \right)} + 24\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=24\).
Find sin α.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(32 \sin{\left(x \right)} + 24 \cos{\left(x \right)} + 24\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=24\).
Find cos α.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(40 \sin{\left(x \right)} + 42 \cos{\left(x \right)} + 25\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=25\).
Find cos α.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(40 \sin{\left(x \right)} + 42 \cos{\left(x \right)} + 25\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=25\).
Find the maximum value of the full expression including D.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
R sin(x+α) and extrema: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(63 \sin{\left(x \right)} + 16 \cos{\left(x \right)} + 26\). Use \(a\sin x+b\cos x=R\sin(x+\alpha)\) with R>0 and \(\displaystyle 0< \alpha < \frac{\pi }{2}\). Here \(\displaystyle D=26\).
Find the maximum value of the full expression including D.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.