Unearthing the sine (sin) in the realm of mathematics calls upon the study of trigonometry, particularly in reference to right-angled triangles. This function represents the ratio of the length of the angle's opposing side in comparison to the length of the hypotenuse. It's also a foundational function when dealing with periodic phenomena as illustrated in mathematics.
| Topic | Problem | Solution |
|---|---|---|
| None | 2. Solve the triangle, given the information belo… | We are given two sides and an included angle. We can use the Law of Sines to find angle C, and then… |
| None | If $\sin \theta=\frac{\sqrt{3}}{2}$, find the deg… | The sine function gives the ratio of the length of the side opposite the angle to the length of the… |
| None | Given $\tan A=-\frac{12}{5}$ and that angle $A$ i… | We are given that \(\tan A = -\frac{12}{5}\) and that angle \(A\) is in Quadrant IV. In this quadra… |
| None | Given $\tan (\theta)=\frac{3}{7}$, find the exact… | Given that \(\tan (\theta) = \frac{3}{7}\), we can assume that \(\sin (\theta) = 3k\) and \(\cos (\… |
| 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… | Let \(a = 2 \tan^{-1} \frac{15}{8}\). Then \(\tan a = \tan(2 \tan^{-1} \frac{15}{8})\). |
| None | Find the exact value of the real number $y$ if it… | The inverse sine function, also known as arcsin, is the inverse function of the sine function. It r… |
| None | Question 2 The cosine of an angle in Quadrant II … | The problem states that the cosine of an angle in Quadrant II is \(-\frac{2}{3}\). |
| None | If $\cos (x)=-\frac{14}{23}$ (in Quadrant-111), f… | Given that \(\cos (x)=-\frac{14}{23}\) (in Quadrant-111), we are asked to find the exact value of \… |
| None | If $\sin (x)=\frac{3}{10}$ (in Quadrant-1), find … | We are given that \(\sin(x) = \frac{3}{10}\) and we are asked to find \(\sin(2x)\). |
| None | An electrician leans an extension ladder against … | Given: angle = $71^\circ$, height = 28 feet |
| None | Find the value of $\sin \theta$, given that $\tan… | Given that $\tan \theta = 1.771$, we need to find the value of $\sin \theta$. We know that $\tan \t… |
| None | 24 A helicopter $H$ is hovering above a straight,… | \(\triangle AHB\) and \(\triangle CHB\) are right triangles with \(\angle AHB = 7^\circ\) and \(\an… |
| None | Find the value of each trigonometric ratio. 5) $\… | \(\sin^2 Z + \cos^2 Z = 1\) |
| None | 2. A telephone pole support must hit the ground a… | Given a telephone pole of height 25 feet and a support wire that makes a $55^\circ$ angle with the … |
| None | Use a table of trigonometric values to find the a… | Given a right triangle with opposite side O = 8 and hypotenuse H = 16, we need to find the angle θ … |
| None | If $\cos \theta=\frac{2}{3}$, then what is the po… | Given that \(\cos \theta = \frac{2}{3}\), we need to find the positive value of \(\sin \frac{1}{2} … |
| None | Write the ratio for $\sin A$. \[ \sin A= \] (Type… | Recall the definition of sine in a right triangle: \(\sin A = \frac{\text{opposite side}}{\text{hyp… |
| None | Use the formula given below to find the area \( K… | \( A = 180 - B - C = 180 - 40 - 70 = 70^{\circ} \) |