Math Jeopardy - Trigonometry

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Aug 21, 2024
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- Math Jeopardy
- Laney College

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Trigonometry

Answer: This is the value of $\cos(\frac{\pi}{2})$ .

Answer: This is the value of $\sin(\frac{\pi}{3})$ .

Answer: This is the value of $\tan(\frac{11\pi}{6})$ .

Answer: This is the value of $\csc(\frac{11\pi}{4})$ .

Answer: This is the value of $\cot(\frac{13247\pi}{333})$ .

Answer: $\sin^2(x)+\cos^2(x)$ always equals this number.

Answer: $\sin(\theta) + \sin(-\theta)$ can be simplified as this very easy expression.

Answer: $\sin(\theta)\cos(\theta)\tan(\theta)\sec(\theta)\csc(\theta)\cot(\theta)$ can be simplified as this very easy expression.

Answer: $\sin^2(x)$ can be written as a fraction with trigonometric expressions without any squares in this way.

Answer: This is the value of $\sin^{-1}(1)$ .

Answer: This is the value of $\tan^{-1}(-\frac{1}{2})$ .

Answer: This is the domain of $\sec^{-1}(x)$ .

Answer: This is how $\sin(\cos^{-1}(x))$ can be written without any trig functions.

Answer: This is how $\cos(\tan^{-1}(x))$ can be written without any trig functions.

Answer: If you increase the angle $\theta$ by a multiple of $2\pi$ , this is how much $\sin(\theta)$ will change.

Answer: If you look at $\tan^{-1}(x)$ for very large values of $x$ this is what the values get close to.

Answer: This is the reason why neither $\sin(\sin^{-1}(x) = x$ nor $\sin^{-1}(\sin(x)) = x$ are true statements for at least some values of $x$ .

Answer: Using the repeated half angle formula, this is what you get when you convert $\sin^4(x)\cos^2(x)$ to an expression that has no powers of trig functions other than 1.

Answer: The graphs of $y=\sin(x)$ and $y=\cos(x)$ intersect at these points.

Answer: These are the values of $x$ where $\csc(x)$ has vertical asymptotes.

Answer: This is the graph of $y=\cos(2x-1)$ .

Answer: This is the graph of $y=1-3\tan(\frac{x+4}{2})$ .

Answer: This is the domain and the range of $\tan^{-1}(x)$ .

Answer: A lifeguard is standing 30 feet from the shore and sees a child drowning 40 feet from the shore and 80 feet from the point, $P$ , on the shore that is closest to the lifeguard. Let $Q$ be the point on the shore that is closest to the drowning child and $x$ be the distance from $P$ to $x$ . Then this first one is the value of the angle from the shoreline the lifeguard runs on the sand and the second one is the value of the angle from the shoreline the lifeguard swims in the water.

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Trigonometry

Answer: This is the value of cos(π2)\cos(\frac{\pi}{2}).

Answer: This is the value of sin(π3)\sin(\frac{\pi}{3}).

Answer: This is the value of tan(11π6)\tan(\frac{11\pi}{6}).

Answer: This is the value of csc(11π4)\csc(\frac{11\pi}{4}).

Answer: This is the value of cot(13247π333)\cot(\frac{13247\pi}{333}).

Answer: sin2(x)+cos2(x)\sin^2(x)+\cos^2(x) always equals this number.

Answer: sin(θ)+sin(−θ)\sin(\theta) + \sin(-\theta) can be simplified as this very easy expression.

Answer: sin(θ)cos(θ)tan(θ)sec(θ)csc(θ)cot(θ)\sin(\theta)\cos(\theta)\tan(\theta)\sec(\theta)\csc(\theta)\cot(\theta) can be simplified as this very easy expression.

Answer: sin2(x)\sin^2(x) can be written as a fraction with trigonometric expressions without any squares in this way.

Answer: This is the statement of the law of sines.

Answer: This is the value of sin−1(1)\sin^{-1}(1).

Answer: This is the value of tan−1(−12)\tan^{-1}(-\frac{1}{2}).

Answer: This is the domain of sec−1(x)\sec^{-1}(x).

Answer: This is how sin(cos−1(x))\sin(\cos^{-1}(x)) can be written without any trig functions.

Answer: This is how cos(tan−1(x))\cos(\tan^{-1}(x)) can be written without any trig functions.

Answer: If you increase the angle θ\theta by a multiple of 2π2\pi, this is how much sin(θ)\sin(\theta) will change.

Answer: These are the trig functions that are even functions.

Answer: If you look at tan−1(x)\tan^{-1}(x) for very large values of xx this is what the values get close to.

Answer: This is the reason why neither sin(sin−1(x)=x\sin(\sin^{-1}(x) = x nor sin−1(sin(x))=x\sin^{-1}(\sin(x)) = x are true statements for at least some values of xx.

Answer: Using the repeated half angle formula, this is what you get when you convert sin4(x)cos2(x)\sin^4(x)\cos^2(x) to an expression that has no powers of trig functions other than 1.

Answer: The graphs of these basic trig functions go through the origin.

Answer: The graphs of y=sin(x)y=\sin(x) and y=cos(x)y=\cos(x) intersect at these points.

Answer: These are the values of xx where csc(x)\csc(x) has vertical asymptotes.

Answer: This is the graph of y=cos(2x−1)y=\cos(2x-1).

Answer: This is the graph of y=1−3tan(x+42)y=1-3\tan(\frac{x+4}{2}).

Answer: This is what SOHCAHTOA stands for.

Answer: This is what "co" means in "cosecant", "cotangent", and "cosine".

Answer: This is the domain and the range of tan−1(x)\tan^{-1}(x).

Answer: A 6 foot person walks on a horizontal road away from a 16 foot tall vertical lamppost. This is the measurement of the downward angle from the lamppost to the person's shadow after the person has walked 8 feet away from the lamppost.

Answer: This is equivalent to 1+tan2(x)1+\tan^2(x), but contains only one term (no ++ or −- signs).

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