The process of resolving standard angle equations is centered around determining the specific measurement of an angle that fulfills a stipulated equation. This generally calls for the usage of algebraic rearrangements, the application of trigonometric identities, and a sound comprehension of the unit circle. The end solutions can be expressed in either degrees or radians, frequently necessitating an understanding of angles situated in varying quadrants.
| Topic | Problem | Solution |
|---|---|---|
| None | Score: $1 / 3$ Penalty: none Question Watch Video… | The given equation is \(\sin \theta=-\frac{\sqrt{2}}{2}\). |
| None | Find the principal root of this equation: \[ \sin… | The principal root of the equation \(\sin(x) = -\frac{1}{2}\) is the value of \(x\) for which the s… |
| None | Determine the solution( $(s)$ for the following w… | First, we need to understand the problem. We are asked to find the solutions for \(x\) in the inter… |
| None | Determine the solution(s) for the following where… | Determine the solution(s) for the following where $0 \pi \leq \alpha \leq 2 \pi$ : $\cos (x)=-\frac… |
| None | Solve for all values of $x$ that satisfy the foll… | Given the equation \(2 \cos ^{2}(x)-3 \cos (x)+1=0\) where \(0 \leq x \leq 2 \pi\) |
| None | How many solutions of the following equation exis… | The solutions to the equation \(\sin(7x) = 0\) are given by \(7x = n\pi\), where \(n\) is an intege… |
| None | Find all solutions to the equation $10 \cos (x+2)… | We have that \(10 \cos (x+2)=2\). |
| None | Solve the equation for exact solutions over the i… | The given equation is \(8 \tan 3 x=8\). |
| None | Solve the equation for exact solutions over the i… | The given equation is \(6 \sin \left(\frac{\theta}{2}\right)=6 \cos \left(\frac{\theta}{2}\right)\)… |
| None | Solve the equation for solutions in the interval … | We are given the equation \(\sin \left(\frac{x}{2}\right)=1-\sin \left(\frac{x}{2}\right)\). |
| 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 | 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 | Find all values of $\theta$ if $\theta$ is in the… | Given that \(\sin \theta \approx 0.4999161\), we need to find all values of \(\theta\) in the inter… |
| None | Find a value of $\alpha$ in $\left[0^{\circ}, 90^… | Given that \(\sec \alpha = 1.3131199\) |
| None | Find a value of $\alpha$ in the interval $\left[0… | The cotangent of an angle is the reciprocal of the tangent of the angle. Therefore, to find the ang… |
| None | Find a value of $\theta$ in the interval $\left[0… | We are given the cosine of an angle and we need to find the angle itself. We can use the arccos fun… |
| None | Solve $\sin A=\frac{\sqrt{3}}{-2}$ if $0 \leq A \… | The given equation is \(\sin A = \frac{\sqrt{3}}{-2}\) with the range of A being \(0 \leq A \leq \p… |
| None | If $\tan \theta=\frac{1}{2},-\frac{\pi}{2}<\theta… | We are given that \(\tan \theta = \frac{1}{2}\) and \(-\frac{\pi}{2}<\theta<\frac{\pi}{2}\). We are… |
| None | Given that $\cos 2 \alpha=\frac{4}{5}$ and $\alph… | We are given that \(\cos 2 \alpha=\frac{4}{5}\) and \(\alpha\) is in quadrant I. |
| None | Find $\sin \theta$. \[ \sec \theta=\frac{13}{6}, … | We know that \(\sec \theta = \frac{1}{\cos \theta}\), so \(\cos \theta = \frac{1}{\sec \theta} = \f… |
| None | Question 8 Difficulty: Ill How many solutions, on… | Find the solutions for the equation \(\tan \theta = 1\) and \(\tan \theta = -1\) in the interval \(… |
| None | $\frac{\sin 8^{\circ}}{16.2}=\frac{\sin \theta}{1… | \(\frac{\sin 8^\circ}{16.2} = \frac{\sin \theta}{10.4}\) |
| None | $17 \tan x>\sqrt{3}$ | Divide both sides of the inequality by 17: \(\tan x > \frac{\sqrt{3}}{17}\) |