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Answer 1 To find the tangent of an angle $ \theta $ on the unit circle, you need to know the coordinates of the point where the terminal side of the angle intersects the unit circle. The coordinates are given by $ ( \cos(\theta), \sin(\theta) ) $.The...
Answer 1 To calculate the total revenue for a hotel in San Diego, we use the formula: $ \text{Total Revenue} = \text{Number of Rooms} \times \text{Occupancy Rate} \times \text{Room Rate} $ LetAnswer 2 To find the total revenue for a hotel in San...
Answer 1 Consider a point on the unit circle at an angle $ \theta $. Using the double-angle identities, we can write: $ \sin(2\theta) = 2\sin(\theta)\cos(\theta) $ and $ \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) $ Thus, $ \tan(2\theta) =...
Answer 1 To find the cosine of the angle $t$ on the unit circle when the sine of $t$ is $\frac{1}{2}$, we can use the Pythagorean identity:\n $ \sin^2(t) + \cos^2(t) = 1 $\n Given that $\sin(t) = \frac{1}{2}$, we substitute and solve for $\cos(t)$:\n...
Answer 1 To find the angle $ \theta $ where the sum of $ \sin(\theta) $ and $ \cos(\theta) $ equals 1.5, we start with the equation: $ \sin(\theta) + \cos(\theta) = 1.5 $ We can use the Pythagorean identity: $ \sin^2(\theta) + \cos^2(\theta) = 1 $...
Answer 1 To find the sine and cosine values for an angle of $ \frac{\pi}{4} $ on the unit circle, we can use the known values of the unit circle. For an angle of $ \frac{\pi}{4} $: $ \sin\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $ $...