📏 trigonometry

1. **State the problem:** Solve the equation $3 + 2\cos^2(\theta) \tan(\theta) = 4 \cos^2(\theta)$ for $0^\circ \leq \theta \leq 360^\circ$. 2. **Recall the definitions and formula

1. **State the problem:** Solve the trigonometric equation $3 + 2\cos^2(\theta)\tan(\theta) = 4\cos^2(\theta)$.\n\n2. **Recall the definitions and formulas:** \n- $\tan(\theta) = \

1. **Express 5 sin x - 3 cos x in the form $R \sin(x - \alpha)$ where $R > 0$ and $0 < \alpha < \frac{\pi}{2}$.** The problem is to rewrite the expression $5 \sin x - 3 \cos x$ as

1. **Express 5 sin x - 3 cos x in the form $R \sin(x - \alpha)$** where $R > 0$ and $0 < \alpha < \frac{\pi}{2}$. 2. The formula to express $a \sin x + b \cos x$ in the form $R \si

1. **Express 5 sin x - 3 cos x in the form $R \sin(x - \alpha)$** where $R > 0$ and $0 < \alpha < \frac{\pi}{2}$. 2. The formula to express $a \sin x + b \cos x$ in the form $R \si

1. **State the problem:** Solve the equation $$2 \cos x - \cos \frac{x}{2} = 1$$ for $$0 \leq x \leq 2\pi$$. 2. **Recall the formula and rules:** We are dealing with trigonometric

1. **Problem statement:** A boat sails from point A due north for 7 km to point B. From B, it sails on a bearing of 100° for 10 km to point C. We need to find the distance from poi

1. The problem asks to evaluate the trigonometric functions for given angles without using a calculator, using the fact that $\pi$ radians equals 180 degrees. 2. Recall the exact v

1. مسئله: حل معادله سکانت سه ایکس یعنی پیدا کردن مقدار $x$ که در آن $\sec(3x)$ تعریف شده و مقدار خاصی دارد. 2. تعریف سکانت: $\sec(\theta) = \frac{1}{\cos(\theta)}$.

1. **Énoncé du problème :** Calculer et simplifier l'expression $$C = 3 \cos^2 34^\circ + \cos 60^\circ + 3 \cos^2 56^\circ$$ et simplifier l'expression $$VD = \frac{\cos y}{\sqrt{

1. **Problem Statement:** Find the difference between $\sin 2x$ and $2 \sin x$. 2. **Recall the formula for double angle sine:**

1. نبدأ ببيان المشكلة: نريد معرفة عدد المرات التي تصل فيها الدالة $$d(x) = \sin(x + 1)$$ إلى قيمتها العظمى في الفترة $$[0, 2\pi]$$. 2. الدالة $$\sin(\theta)$$ تصل إلى قيمتها العظمى

1. نبدأ بتحديد المشكلة: نريد معرفة عدد نقاط تقاطع منحني الدالة $d(x) = \cos(2x)$ مع محور السينات في الفترة $[0, 2\pi]$. 2. نقاط تقاطع المنحني مع محور السينات تحدث عندما تكون قيمة ا

1. نبدأ بقراءة السؤال: د(س) = 2 جَأ س + 1 2. د(س) هي دالة جيب تمام مضروبة في 2 ثم أضيف إليها 1.

1. **State the problem:** Find the value of $\sin 135^\circ$. 2. **Recall the formula and rules:** The sine of an angle in degrees can be found using the unit circle or sine additi

1. **State the problem:** Find the values of $\sin 135^\circ$ and $\tan 15^\circ$. 2. **Recall formulas and important rules:**

1. The problem is to evaluate $\cos \frac{2\pi}{3}$.\n\n2. Recall that the cosine function for an angle $\theta$ in radians is the x-coordinate of the point on the unit circle at t

1. Let's start by stating the problem: You want to learn about the inverse trigonometric functions arcsin, arccos, and arctan. 2. These functions are the inverses of the sine, cosi

1. ප්‍රශ්නය: A + B = 45° නම්, (1 + \tan A)(1 + \tan B) = 2 බව සනාථ කරන්න. 2. අපිට දැනගත යුතුයි: \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}.

1. **State the problem:** Solve the equation $$1 + \frac{\sin x}{\cos x} = \frac{\cos x}{1 - \sin x}$$ for $x$. 2. **Rewrite the equation:** Note that $\frac{\sin x}{\cos x} = \tan

1. **State the problem:** Solve the equation $\sin 2x = \sin x$ for $x$.\n\n2. **Recall the formula and rules:** The equation $\sin A = \sin B$ implies that either:\n\n$$A = B + 2k