📏 trigonometry

1. **State the problem:** Find the value of $\arccos\left(\frac{4}{3 \times \sqrt{2}}\right)$. 2. **Recall the domain of arccos:** The function $\arccos(x)$ is defined only for $x$

1. **State the problem:** Find the value of $\arccos\left(\frac{4}{3} \times \sqrt{2}\right)$. 2. **Recall the domain of arccos:** The function $\arccos(x)$ is defined only for $x$

1. **State the problem:** Solve the trigonometric equation $3 \sin \theta - 4 \cos \theta = 2$ for $\theta$. 2. **Formula and approach:** We use the identity that any expression of

1. **State the problem:** Find the real solutions for the equations: (a) $3 \sin \theta - 4 \cos \theta = 2$,

1. **State the problem:** We need to sketch one cycle of the function $$f(x) = 3\cos 2(x - 30^\circ) - 2$$ using transformations, then find its domain and range.

1. The problem is to evaluate $\sin(4)$.\n\n2. The sine function, $\sin(x)$, gives the ratio of the opposite side to the hypotenuse in a right triangle for an angle $x$ measured in

1. **Problem:** Simplify the expression $ (1 - \cos\theta)(1 + \cos\theta) $. 2. **Formula:** Use the difference of squares identity: $ (a - b)(a + b) = a^2 - b^2 $.

1. **Énoncé du problème :** Calculer l'expression $$\cos^2(45^\circ) - \sin^2(-270^\circ) \times \tan^2(240^\circ)$$ sans calculatrice. 2. **Rappel des formules et règles important

1. Énonçons le problème : On a l'équation $8 \tan x = 3 \cos x$ avec $0^\circ < x < 180^\circ$. Il faut déterminer la valeur de $\sin x$. 2. Rappelons que $\tan x = \frac{\sin x}{\

1. **State the problem:** A 5.5-foot tall man is standing with the sun shining at an angle of depression of 55°. We need to find the length of his shadow.

1. **Énoncé du problème :** Philippe veut fixer un panier de basket à une hauteur réglementaire de 3,05 m.

1. The problem asks to evaluate the expression a) $\tan 2x$ for $\pi \leq x \leq \frac{3\pi}{2}$ given $\cos x = \frac{2}{45}$.\n\n2. Recall the double angle formula for tangent: $

1. **State the problem:** We want to write an equation equivalent to \(y = -6\cos\left(x + \frac{\pi}{2}\right) + 4\) using the sine function. 2. **Recall the trigonometric identit

1. **State the problem:** Prove the trigonometric identity $$\sec^4 x - 1 = 2 \tan^2 x + \tan^4 x.$$\n\n2. **Recall the fundamental identity:** $$\sec^2 x = 1 + \tan^2 x.$$ This is

1. **State the problem:** Susan is at the top of a 2.1 m high wall at the edge of an 8 m wide beach. She measures the angle of depression to a swimmer in the sea as 6°. We need to

1. **State the problem:** Solve the equation $\left(c \sin x + \cos x\right)^2 = 2$ for $x$. 2. **Recall the formula and rules:** The square of a sum is expanded as $\left(a+b\righ

1. Énonçons le problème : Résoudre sur l'intervalle $]-\pi; \pi]$ le système d'inéquations : $$\cos(x) \leq -\frac{\sqrt{2}}{2}$$

1. The problem is to understand the basics of trigonometry, which deals with the relationships between the angles and sides of triangles. 2. The fundamental formulas in trigonometr

1. Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles. 2. The primary functions in trigonometry are sine ($\sin$), c

1. **State the problem:** We need to solve for the angle $x$ in a triangle with sides given as 4.6, 9, and an unknown side opposite $x$. 2. **Identify the formula:** Use the Law of

1. **State the problem:** We have a right triangle with a right angle at P, a horizontal side PQ = 5.1, a hypotenuse QO = 8.9, and we need to find the angle $x^\circ$ at vertex O.