| Topic | Problem | Solution |
|---|---|---|
| None | Solve the equation for exact solutions over the i… | The equation \(\sin (3 \theta)=-1\) implies that \(3\theta\) is an angle whose sine is -1. |
| None | Solve the equation for exact solutions in the int… | The given equation is \(6 \sec ^{2} \theta \tan \theta=8 \tan \theta\). |
| None | Solve the equation for solutions over the interva… | Given the equation \(\csc ^{2} \theta-2 \cot \theta=0\), we need to solve for \(\theta\) over the i… |
| None | Solve the equation for solutions in the interval … | The given equation is a product of two factors equal to zero. This means that either of the factors… |
| None | Solve the equation for exact solutions over the i… | We can write the equation as \[3 \frac{\cos x}{\sin x} + 2 = 5.\] |
| None | Use the unit circle shown here to solve the trigo… | The sine function gives the y-coordinate of the point on the unit circle that is an angle of \(\the… |
| None | Use the unit circle shown here to solve the trigo… | The given equation is \(\cos x = \frac{1}{2}\). We need to find the solutions over the interval \([… |
| None | Write the expression as an algebraic (nontrigonom… | Write the expression as an algebraic (nontrigonometric) expression in $u$, for $u>0$. |
| None | Write each expression as an algebraic (nontrigono… | Given the expression \(\sin \left(2 \sec ^{-1} \frac{u}{6}\right)\), we need to convert it into an … |
| None | Write the expression as an algebraic (nontrigonom… | Given the trigonometric expression \(\tan (\arccos u)\), we are asked to express it in terms of \(u… |
| None | Give the exact value of the expression without us… | Given the expression \(\cos \left(\tan ^{-1} \frac{4}{3}-\tan ^{-1}\left(-\frac{8}{15}\right)\right… |
| None | Give the exact value of the expression without us… | The given expression is in the form of \(\sin(2\theta)\), where \(\theta = \cos^{-1}(\frac{1}{5})\)… |
| None | Give the exact value of the expression without us… | The given expression is in the form of cosine of double angle. We can use the identity of cosine of… |
| None | Give the exact value of the expression without us… | Let \(a = 2 \tan^{-1} \frac{15}{8}\). Then \(\tan a = \tan(2 \tan^{-1} \frac{15}{8})\). |
| None | Give the exact value of the expression without us… | The expression is asking for the cosine of the angle whose tangent is -2. |
| None | Use a calculator to find $\arctan (0.490)$ $\arct… | The question is asking for the arctan of 0.490. The arctan function is the inverse of the tangent f… |
| None | Use a calculator to give the real number value. (… | The problem is asking for the inverse sine (also known as arcsine) of -0.2210. The inverse sine fun… |
| None | Use a calculator to give the real number value. (… | The problem is asking for the arccosine of 0.721. The arccosine function, also known as the inverse… |
| None | Use a calculator to find the value in decimal deg… | Given the value is -0.9593. |
| None | Give the degree measure of $\theta$ if it exists.… | Given that \(\theta=\cos^{-1}(2)\) |
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