| Topic | Problem | Solution |
|---|---|---|
| None | Find $x$, the angle of depression from the top of… | Given that the height of the lighthouse is 194 ft and the distance to the ship is 1011 ft, we can u… |
| None | Convert the following angle to decimal degrees. \… | The given angle is in degrees, minutes, and seconds. To convert this to decimal degrees, we need to… |
| None | Simplify the expression by using a double-angle f… | Given the expression \(\cos ^{2} 2 \theta-\sin ^{2} 2 \theta\). |
| None | Find all solutions of the equation in the interva… | Rewrite the given equation \(\sec \theta-1=0\) as \(\frac{1}{\cos \theta} - 1 = 0\) |
| None | Prove that : $\frac{3 \omega-1}{\omega^{2}-2 i}=1… | Given the complex number equation: \(\frac{3 \omega-1}{\omega^{2}-2 i}=1+2 \omega i\) |
| None | Simplify the expression by using a double-angle f… | Given the expression \(2 \sin 5 \theta \cos 5 \theta\). |
| None | Complete the square and write the given equation … | Given equation is \(x^2+y^2+8x-2y-19=0\). |
| None | Simplify the expression by using a double-angle f… | The given expression is \(\frac{2 \tan \frac{\pi}{9}}{1-\tan ^{2} \frac{\pi}{9}}\) |
| None | $1 \leftarrow \quad$ Use the compound interest fo… | Given the principal amount (P) as $1000, the annual interest rate (r) as 0.05, the time in years (t… |
| None | Looking up, Chang sees two hot air balloons in th… | Given that the lower hot air balloon is 810 meters away, at an angle of $19^{\circ}$ from the verti… |
| None | Find the exact value of $\cos \frac{5 \pi}{12}$ b… | First, we need to express \(\frac{5 \pi}{12}\) as a sum or difference of angles that we know the co… |
| None | Suppose that the local sales tax rate is $4 \%$ a… | Suppose that the local sales tax rate is 4% and you purchase a car for $26,500. |
| None | Find the exact value of $\tan ^{-1}(\cos \pi)$. W… | The problem is asking for the inverse tangent of the cosine of pi. The cosine of pi is -1. So, we n… |
| None | A lighthouse sits at the edge of a cliff, as show… | Given that the distance from the ship to the base of the cliff is 825 meters, the angle of elevatio… |
| None | Boris is sitting in a movie theater, 8 meters fro… | Given that Boris is sitting in a movie theater, 8 meters from the screen. The angle of elevation fr… |
| None | (14) A product design team is working on a new dr… | Given: Volume = 225 cm³, Height = 12.5 cm, Length = 4.5 cm |
| None | A ramp $13 \mathrm{ft}$ long rises to a platform … | The problem is asking for the angle of elevation of the ramp. This is a trigonometry problem, and w… |
| None | An architect designs two houses that are shaped a… | The given equation is of a hyperbola. The standard form of a hyperbola is \(\frac{x^2}{a^2} - \frac… |
| None | A ladder leans against the side of a house. The a… | Given that the angle of elevation of the ladder is $75^{\circ}$ and the bottom of the ladder is $9 … |
| None | Use the diagram in the box to convert the given m… | Given that 1 meter is equal to 100 centimeters. |
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