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Magazine Problem 20
In \(15-20,\) find, to the nearest degree, the measure of an acute angle for which the given equation is true. $$ \cot \theta+8=3 \cot \theta+2 $$
Problem 20
In \(15-20\) , find, to the nearest hundredth of a radian, the values of \(\theta\) in the interval \(0 \leq \theta<2 \pi\) that satisfy the equation. $$ 2 \cot ^{2} \theta-13 \cot \theta+6=0 $$
Problem 21
In \(21-24,\) find, to the nearest tenth, the degree measures of all \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that make the equation true. $$ 8 \cos \theta=3-4 \cos \theta $$
Problem 21
Find the smallest positive value of \(\theta\) such that \(4 \sin ^{2} \theta-1=0\)
Problem 22
Find, to the nearest hundredth of a radian, the value of \(\theta\) such that \(\sec \theta=\frac{5}{\sec \theta}\) and \(\frac{\pi}{2} < \theta < \pi\)
Problem 22
In \(21-24,\) find, to the nearest tenth, the degree measures of all \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that make the equation true. $$ 5 \sin \theta-1=1-2 \sin \theta $$
Problem 23
In \(21-24,\) find, to the nearest tenth, the degree measures of all \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that make the equation true. $$ \tan \theta-4=3 \tan \theta+4 $$
Problem 23
Find two values of \(A\) such that \((\sin A)(\csc A)=-\sin A\)
Problem 24
In \(21-24,\) find, to the nearest tenth, the degree measures of all \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that make the equation true. $$ 2-\sec \theta=5+\sec \theta $$
Problem 25
In \(25-28,\) find, to the nearest hundredth, the radian measures of all \(\theta\) in the interval \(0 \leq \theta<2 \pi\) that make the equation true. $$ 10 \sin \theta+1=3-2 \sin \theta $$
