📏 trigonometry

1. **Problem Statement:** Find the sine, cosine, and tangent of angle $S$ in the right triangle $TUS$ where $US=16$, $TS=34$, and angle $U$ is the right angle. 2. **Recall definiti

1. **Problem Statement:** Find the cosecant of angle $H$ in right triangle $GHF$ where $\angle F$ is the right angle, $GF = 7\sqrt{3}$, and $FH = 7$. 2. **Recall the definition:**

1. **Problem Statement:** Find the cosecant of angle $C$ in the right triangle $CDB$ where $\angle D$ is the right angle. 2. **Given:**

1. **Problem Statement:** Find the secant of angle $E$ in right triangle $FDE$ where $\angle F$ is the right angle. The sides are given as $FD = 2\sqrt{3}$ (adjacent to $E$), $ED =

1. **State the problem:** We need to find the cosecant of angle $W$ in right triangle $V X W$ where $\angle X$ is the right angle. 2. **Identify sides relative to $\angle W$:**

1. **State the problem:** We are given two right-angled triangles QRU and RSV with angles $x^\circ$ and $y^\circ$ respectively, where $\sin x^\circ = \frac{3}{5}$ and $\tan y^\circ

1. **Stating the problem:** We are given the function $y = 2 \sin x$ and need to analyze its graph characteristics and verify the truth of several statements about amplitude, maxim

1. **State the problem:** We have a right triangle with a hypotenuse of length 5, an angle of 125° outside the triangle, and legs labeled $x$ (horizontal) and $y$ (vertical). We ne

1. **State the problem:** We have a right triangle with hypotenuse 13, an angle of 35°, and sides labeled $x$ (horizontal) and $y$ (vertical). We need to find $x$ and $y$ rounded t

1. **Problem statement:** We need to find the length of the walking trail BC in triangle ABC where angle A = 54°, angle B = 65°, and side AC = 7 km. 2. **Formula and rules:** Use t

1. **State the problem:** We are given the function $y = 3\sin\theta - 2$ and need to find its domain, range, amplitude, period, phase shift, and vertical slide. 2. **Recall the ge

1. **State the problem:** We have a trigonometric model for the depth of water in a marina given by $$d(t) = 8 + 5\sin\left(\frac{\pi t}{6}\right)$$ where $t$ is hours from midnigh

1. The problem is to understand and analyze the function $\sin x$. 2. The sine function is a fundamental trigonometric function defined for all real numbers $x$ and is periodic wit

1. Probleem: Combineer de uitspraken uit de eerste kolom (A t/m E) met de juiste uit de tweede kolom (1 t/m 7) zodat er een ware wiskundige uitspraak ontstaat. 2. Formules en regel

1. **Probleem 1: Bereken de ontbrekende waarden in driehoek ABC** Gegeven: driehoek ABC is rechthoekig in C, |AB| = 10 cm, hoek A = 42°13'44".

1. **State the problem:** Find the exact value of $\cos 75^\circ$ using the formula for the cosine of a sum of angles. 2. **Recall the formula:**

1. **State the problem:** Calculate the value of $$\frac{\sin(73)}{\sin(76)} \times 9.6$$. 2. **Recall the formula:** We use the sine function values and multiply the fraction by 9

1. **State the problem:** We have a right triangle ABC with angle C = 90 degrees, hypotenuse AB = 39, adjacent side AC = 36, and opposite side BC = 15. We need to find $\tan A$. 2.

1. **Problem:** Find the distance between the base of the telephone pole and the base of the tree given the angle of depression is 63° and the pole height is 18 ft. 2. **Formula:**

1. **Problem Statement:** From a 14 m high tower, the angles of depression to two houses are 7° and 4°. We need to find the distance between the houses under three scenarios:

1. **Problem:** Markiere die Winkel 45°, 90°, 270°, 315° auf dem Sinusgraphen. 2. **Problem:** Bestimme für welche Winkel \(\alpha\) gilt \(\sin(\alpha) = 0{,}5\) und \(\sin(\alpha