📏 trigonometry

1. **State the problem:** Given angles $\angle R = 46^\circ$, $\angle S = 85^\circ$, $\angle T = 38^\circ$, and side $t = 17$, find side $s$ using the Law of Sines. 2. **Recall the

1. **State the problem:** Given a triangle with sides and angles, find the measure of angle $T$ when $s=42$, $t=29$, and $m \angle S=63^\circ$ using the Law of Sines.

1. The problem asks to rotate the angle $\frac{13\pi}{4}$ radians to an equivalent angle within $\frac{\pi}{18}$ radians. 2. To solve this, we use the fact that angles differing by

1. Énonçons le problème : Trouver les coordonnées des zéros de la fonction $$f(x) = 2 \cos(\pi (x+2)) - 1$$ pour $$x \in \mathbb{R}$$. 2. Rappelons que les zéros d'une fonction son

1. Énoncé du problème : Trouver les zéros de la fonction $$f(x) = 2 \cos \pi (x + 2) - 1$$ pour $$x \in \mathbb{R}$$. 2. Pour trouver les zéros, on résout $$f(x) = 0$$ :

1. Énoncé du problème : Trouver les valeurs de $x \in \mathbb{R}$ telles que $f(x) = -2 \cos\left(\frac{5\pi}{6}(x+1)\right) - 3 = 0$. 2. Isolons le cosinus :

1. **State the problem:** We are given the function $$f(x) = 4 \cos\left(4\pi \left(x + \frac{1}{6}\right)\right) - 3$$ and want to understand its key features such as amplitude, p

1. Énonçons le problème : Trouver les zéros de la fonction $$f(x) = -2 \sin\left(\frac{5\pi}{6}(x+1)\right) - 3$$ pour $$x \in \mathbb{R}$$. 2. Rappelons que les zéros d'une foncti

1. **Problem:** Find the length of side $x$ in a right triangle where the angle is $54^\circ$ and the adjacent side is 22. 2. **Formula:** Use the sine definition: $\sin(\theta) =

1. **State the problem:** We need to find the value of $\cos W$ in a right triangle with vertices $X$, $W$, and $Y$, where the right angle is at $X$. The side $XY$ (opposite to ang

1. **State the problem:** We need to find the value of $\sin Z$ in the right triangle with vertices $Y$, $Z$, and $X$, where the right angle is at $Y$. 2. **Identify the sides:** T

1. **Stating the problem:** We need to find $\cot(30^\circ + \alpha)$ given that $\cot \alpha = 2$. 2. **Formula used:** The cotangent addition formula is

1. **Problem:** Find the missing side $x$ in a right triangle with angle $54^\circ$, adjacent side $22$, and hypotenuse $H$. 2. **Formula:** Use cosine ratio since adjacent and hyp

1. **Problem:** Find $\sec\left(\frac{5\pi}{4}\right)$.\n\n2. **Recall the definition:** $\sec \theta = \frac{1}{\cos \theta}$.\n\n3. **Evaluate $\cos\left(\frac{5\pi}{4}\right)$:*

1. **State the problem:** We have a right triangle with legs 16 cm and 20 cm, and we need to find the measure of angle C opposite the 16 cm side. 2. **Formula used:** To find an an

1. **Problem (a):** Find $A$, $B$, and $n$ for the curve $y = A + B \sin(nt)$ given the sine wave starts at $y=6$ when $t=0$ and oscillates with zero crossings near $\frac{\pi}{4}$

1. **State the problem:** We have a right triangle VWU with a right angle at W. Side VW = 33 units, side VU = 68 units, and we want to find $\sin(V)$, $\cos(V)$, and $\tan(V)$ for

1. **State the problem:** We are given that $\sin(\ln x) = \frac{1}{4}$ and $\sin(\ln y) = \frac{1}{7}$ with $0 < \ln x < \frac{\pi}{2}$ and $0 < \ln y < \frac{\pi}{2}$. We need to

1. The problem is to calculate $2.0 \tan 35^\circ$. 2. Recall the formula: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ in a right triangle, but here we just need the ta

1. **Problem Statement:** Sketch the graph of the function $y = 2 \sin x$ for $0 \leq x \leq 2\pi$. 2. **Formula and Rules:** The sine function $\sin x$ oscillates between $-1$ and

1. **Problem Statement:** A fire ranger is at the top of a 90-ft observation tower. He sees two fires: one due west at an angle of depression of 5°, and another due south at an ang