| Topic | Problem | Solution |
|---|---|---|
| None | Use identities to find values of the sine and cos… | We are given that \(\sin \theta = -\frac{\sqrt{6}}{7}\) and \(\cos \theta > 0\). |
| None | Given that $\cos \alpha=\frac{3}{5}$ and $0<\alph… | We are given that \(\cos \alpha=\frac{3}{5}\) and \(0<\alpha<\frac{\pi}{2}\). We need to find the v… |
| None | Use identities to find values of the sine and cos… | We are given that \(\tan x = -3\) and \(\cos x < 0\). We are asked to find \(\cos 2x\). We know tha… |
| None | Use identities to fill in the blank with the appr… | Use identities to fill in the blank with the appropriate trigonometric function name. \[\cos 35^{… |
| None | Use the cofunction identities to find an angle $\… | The cofunction identities in trigonometry state that the secant of an angle is equal to the cosecan… |
| None | Write the expression in terms of sine and cosine,… | The given expression is \(\cos \beta - \sec \beta\). |
| None | Use the cosine of a sum and cosine of a differenc… | We are given that \(\sin s = \frac{5}{13}\) and \(\sin t = -\frac{3}{5}\), and that s is in quadran… |
| None | Factor the following expression. \[ 2 x^{2}-7 x+6… | The given expression is a quadratic equation of the form \(ax^2 + bx + c\). |
| None | Verify that the equation given below is an identi… | We are given the equation \(\cos 2 x=\frac{\cot ^{2} x-1}{\cot ^{2} x+1}\) and asked to verify that… |
| None | Find the \( 6^{\text {th }} \) partial sum of the… | \( S_{6} = \frac{a_{1}(1 - r^{6})}{1 - r} \) |
| None | Use the cosine of a sum and $\operatorname{cosine… | Given that $\cos s=-\frac{4}{5}$ and $\sin t=\frac{2}{5}$, we can use the Pythagorean identity to f… |
| None | Perform the indicated operation and simplify the … | Given the expression \(\frac{\cos \theta}{\sec \theta}+\frac{\sin \theta}{\csc \theta}\) |
| None | Factor the following trinomial. \[ 36 x^{2}-72 x+… | The given trinomial is a quadratic equation of the form \(ax^2 + bx + c\). |
| None | Factor the trigonometric expression. \[ 25 \sec ^… | Rewrite the given trigonometric expression as a quadratic equation in terms of sec^2(w). It can be … |
| None | Perform the indicated operation and simplify the … | Rewrite the expression as follows: \(\frac{1}{\tan x}(\tan x - \frac{1}{\cos x})\) |
| None | Factor the trigonometric expression completely. \… | Factor the trigonometric expression completely: \(\csc ^{2} w-\tan ^{2} x\) |
| None | A survey showed that $78 \%$ of adults need corre… | This is a binomial probability problem. We are given that the probability of success (an adult need… |
| None | Find $\sin \theta$ \[ \tan \theta=-\frac{\sqrt{10… | Given that \(\tan \theta = -\frac{\sqrt{10}}{3}\) and \(\cos \theta > 0\) |
| None | What are the two decisions that you can make from… | The two decisions that can be made from performing a hypothesis test are to either reject the null … |
| None | Write the expression in terms of sine and cosine,… | Given the expression \(\sin \alpha(\csc \alpha-\sin \alpha)\) |
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