Question 27
Difficulty: ★☆☆\(\csc^2 x = 4\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees. For example, \(-60^\circ\) should be entered as -60Question 28
Difficulty: ★☆☆\(\sec^2 x = 9\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 29
Difficulty: ★☆☆\(9\cot^2\!\big(\tfrac{x}{2}\big)=4\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 30
Difficulty: ★☆☆\(\sec x=\cos x\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60^\circ\) should be entered as -60Question 31
Difficulty: ★☆☆\(\csc x=\sec x\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60^\circ\) should be entered as -60Question 32
Difficulty: ★☆☆\(2\tan x=3\csc x\quad\text{for }-180^\circ \le x \le 180^\circ.\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60^\circ\) should be entered as -60Question 33
Difficulty: ★☆☆\(2\tan^2\theta-1=\sec\theta\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 34
Difficulty: ★★☆\(3\csc^2\theta=13-\cot\theta\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 35
Difficulty: ★★☆\(2\cot^2\theta-\csc\theta=13\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 36
Difficulty: ★★☆\(\csc\theta+\cot\theta=2\sin\theta\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60^\circ\) should be entered as -60Question 37
Difficulty: ★★☆\(\tan^2\theta+3\sec\theta=0\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 38
Difficulty: ★★☆\(\sqrt3\,\sec^2\theta=\csc\theta\quad(0^\circ\le\theta\le360^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 39
Difficulty: ★★☆\(\sec\theta=3\cos\theta-\tan\theta\quad(0^\circ\le\theta\le180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 40
Difficulty: ★★☆\(2\sec^2(2\theta)=3\tan(2\theta)+1\quad(0^\circ\le\theta\le180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 41
Difficulty: ★★☆\(\sec^4\theta+2=6\tan^2\theta\quad(0^\circ\le\theta\le180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60^\circ\) should be entered as -60Question 42
Difficulty: ★★☆\(2\cot^2(2\theta)+7\csc(2\theta)=2\quad(0^\circ\le\theta\le180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 43
Difficulty: ★★☆\(\tan^2\theta+3\sec\theta+3=0\quad(0\le\theta\le2\pi).\)
Enter your answer in terms of \(\pi\) in exact form. For example, enter \(\pi/3\) as 1/3.Question 44
Difficulty: ★★☆\(3\cot^2\theta+5\csc\theta+1=0\quad(0\le\theta\le2\pi).\)
Enter your answer in terms of \(\pi\) in exact form. For example, enter \(\pi/3\) as 1/3.Question 45
Difficulty: ★★★\(6\sec^{3}\theta-5\sec^{2}\theta-8\sec\theta+3=0\quad(0^\circ\le \theta\le 180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5Question 46
Difficulty: ★★★\(2\cot^{3}\theta+3\csc^{2}\theta-8\cot\theta=0\quad(0^\circ\le \theta\le 180^\circ).\)
Enter your answer in degrees, rounded to 1 decimal place. For example, \(-60.5^\circ\) should be entered as -60.5