📏 trigonometry

1. Problem: Calculate the inverse tangent (arctan) values for given numbers and fractions. 2. Formula: The inverse tangent function is defined as $\tan^{-1}(x)$ which gives the ang

1. **State the problem:** Solve the trigonometric equation $$2 \cos^2 x + \cos 4x = 0$$. 2. **Recall formulas and identities:**

1. **Stating the problem:** We are given two equations:

1. Mari kita buktikan identitas \( \frac{\cot \theta + \tan \beta}{\cot \beta + \tan \theta} = \cot \theta \tan \beta \).\n 2. Ingat definisi: \( \cot x = \frac{\cos x}{\sin x} \)

1. **State the problem:** Given triangle ABC with angles $A=41^\circ$, $B=82^\circ$, and side $a=56$, find the missing angle $C$ and sides $b$ and $c$. 2. **Use the triangle angle

1. **Énoncé du problème :** On a l'équation $$\sin x + 2 \cos x = 0$$.

1. **Problem Statement:** We need to find the sine of angle $T$ in a right triangle where the side opposite $T$ is 20 units, the hypotenuse is 52 units, and the adjacent side is 48

1. **Problem Statement:** We need to find the tangent of angle $X$ in a right triangle with sides $VW=77$, $WX=85$ (hypotenuse), and side $VX$ unknown. 2. **Formula:** The tangent

1. **Problem statement:** Find the tangent of angle $B$ in a right triangle with vertices $A$, $B$, and $C$, where $AC=15$, $BC=17$, and angle $A$ is $90^\circ$. 2. **Recall the de

1. **Problem Statement:** A surveyor in an airplane observes two points A and B on opposite shores of a lake. The angles of depression to points A and B are 32° and 45°, respective

1. Problem statement: In the right triangle with vertices G (top-left), F (bottom-left), and H (bottom-right), the side GF is the opposite side with length 6 and the side FH is the

1. **State the problem:** We have a right triangle with hypotenuse 18.7 cm, vertical side 15.2 cm, and we need to find angles $x$ and $y$. 2. **Identify the sides:** The right angl

1. **State the problem:** We are given two acute angles $X$ and $Y$ with $Y = 32^\circ$ and the equation $\frac{\sin X}{\cos Y} = 1$. We need to find the measure of angle $X$ in de

1. **State the problem:** We need to find the length $x$ of the side opposite the 49° angle in a triangle where one side is 6 cm and the angles are 49° and 60°. 2. **Identify the t

1. **Problem statement:** We have a triangle with angles 44° and 60°, and a side of length 11 cm opposite the 44° angle. We need to find the length $x$ opposite the 60° angle. 2. *

1. **مشكلة د(س) = ٣ - ٢|حال(س + \frac{\pi}{6})** حيث \( \frac{\pi}{6} \geq س \geq \lambda ك \) مع \( ك \) عدد طبيعي. المطلوب: تحديد ظل الشكل المقترن بأكبر قيمة لـ \( ك \) حيث تكون

1. **مشكلة:** لدينا تعبيرات رياضية متعددة تتعلق بدوال مثلثية وعلاقات بينها، ونريد تحديد الظل أو القيمة المرتبطة بكل شكل أو تعبير. 2. **مراجعة القواعد:**

1. **Problem statement:** We need to find the size of angle $x$ in a right-angled triangle where the side opposite to $x$ is 6.4 m and the hypotenuse is 9.3 m. 2. **Formula used:**

1. Problem: Evaluate each trigonometric expression without using a calculator or table. 2. Recall key values and identities:

1. **State the problem:** In triangle ABC, given that $\cot A \cdot \cot B = \frac{1}{2}$ and $\cot B \cdot \cot C = \frac{1}{18}$, find the value of $\tan B$. 2. **Recall the tria

1. Let's start by understanding the problem: you want to solve a trigonometric expression by taking common factors $h_1$ and $h_2$. 2. The general approach is to factor out the com