Arcs and angles, signs, extreme values, domain, period and graphs of circular functions (chapters I and II). Teste 1ITA-72 The convex angle formed by the hour and minute hands at 10 hours and 15 minutes is: a) $142^\circ 30'$b) $142^\circ 40'$c) $142^\circ$d) $141^\circ 30'$e) none of the previous answers At 10 h 15 min, the minute hand is at $90^\circ$ (from 12) and the hour hand is at $300^\circ + 15 \cdot 0{,}5^\circ = 307^\circ 30'$. The difference is $217^\circ 30'$, whose complement is $142^\circ 30'$. Teste 2FUVEST-77 The acute angle formed by the hands of a clock at 1 hour and 12 minute is: a) $27^\circ$b) $30^\circ$c) $36^\circ$d) $42^\circ$e) $72^\circ$ The minute hand moves $6^\circ$ per minute and the hour hand moves $0{,}5^\circ$. At 1 h 12 min: minutes in $72^\circ$, hours in $30^\circ + 6^\circ = 36^\circ$; the angle is $36^\circ$.
Response graphs show a complete period; the dashed curve, when it appears, is the “reference” function ($\operatorname{sen} x$ or $\cos x$). To check your graph, also use $a + b\operatorname{sen}(cx + d)$ explorer. Sine function In exercises 23 to 42, determine the period and the image and plot the graph of a complete period of the given function $f\colon \mathbb{R} \to \mathbb{R}$. 23 $f(x) = -\operatorname{sen} x$. See the resolutionWe build a table in three steps: 1st) we assign values to $x$; 2nd) we associate the value of $\operatorname{sen} x$ to each $x$; 3rd) we multiply $\operatorname{sen} x$ by $-1$. $x$ $0$ $\frac{\pi}{2}$ $\pi$ $\frac{3\pi}{2}$ $2\pi$ $\operatorname{sen} x$ $0$ $1$ $0$ $-1$ $0$ $y$ $0$ $-1$ $0$ $1$ $0$ With this table we obtain 5 points of the graph, which is the symmetric of the sinusoid in relation to the $x$ axis. It is immediate that $\operatorname{Im}(f) = [-1, 1]$ and $p(f) = 2\pi$. Ative o JavaScript para ver esta figura interativa.