📏 trigonometry

1. Convert from degrees to radians. The formula to convert degrees to radians is:

1. সমস্যাটি হলো: $\sin 2\theta = \frac{1}{2}$ হলে, $\theta$ এর মান নির্ণয় করতে হবে। 2. সূত্র: $\sin 2\theta = \frac{1}{2}$

1. **Problem Statement:** Given a right triangle with hypotenuse 35, vertical leg 21 adjacent to angle X, and horizontal leg 20 adjacent to angle Z, find the six trigonometric rati

1. **State the problem:** We need to find the value of $$\cos\left(\tan^{-1}\left(\frac{8}{15}\right) + \tan^{-1}\left(\frac{15}{8}\right)\right)$$ where both angles are from the r

1. **Problem statement:** Find the value of $\theta$ given:

1. **State the problems:** - Evaluate $f(x) = 8 \sin x - 4 \cos \frac{x}{2}$ at $x = \frac{\pi}{3}$.

1. **Problem 1:** Evaluate $\sin^2 25^\circ + \sin^2 65^\circ$. 2. Use the identity $\sin^2 \theta + \cos^2 \theta = 1$ and note that $65^\circ = 90^\circ - 25^\circ$, so $\sin 65^

1. **Problem Statement:** Evaluate $\sin t$, $\cos t$, and $\tan t$ for $t = -\frac{5\pi}{4}$.\n\n2. **Recall the definitions and formulas:**\n- $\sin t$ and $\cos t$ are the sine

1. **State the problem:** We need to find the exact value of the function $$f(x) = \sin(x) + 3 \tan(x)$$ at $$x = \frac{2\pi}{3}$$. 2. **Recall the definitions and values:**

1. **Énoncé du problème :** Francine et Robert observent un cerf-volant sous des angles d'élévation respectifs de 24° et 55°. La distance entre Francine et le cerf-volant est de 13

1. Énoncé du problème : Francine et Robert observent un cerf-volant sous des angles d'élévation respectifs de 24° et 55°. La distance entre Francine et le cerf-volant est de 13,68

1. **Problem 1: Find the hypotenuse k in triangle JKL** Given: right angle at K, side l (opposite ∠L) = 15, angle ∠J = 35°.

1. **State the problem:** We need to find the two smallest positive values of $p$ such that $$\sin(4.08p + 12.40) \cdot \tan(2.45p + 17.17) = 0.$$ 2. **Understand the equation:** T

1. **Solve for the indicated value (right angle triangle):** 1.a) Given $\sin \theta = \frac{4}{7}$, find $\theta$.

1. The problem is to verify the trigonometric identity involving the sine of sums and differences. 2. We start with the expression $$\sin\frac{A+B}{2}$$ and substitute it as $$\sin

1. **State the problem:** We want to show that $$\sin A + \sin B + \sin C = 4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}$$ given that $$A + B + C = \pi$$. 2. **Recall the s

1. **Problem Statement:** We need to find which equation correctly models the height $H(t)$ of a rider on the London Eye as a function of time $t$ in minutes. 2. **Given Informatio

1. **Problem 1: Write an equation for the height $h$ of a point on the Ferris wheel as a function of time $t$.** Given:

1. **Problem Statement:** We are given a cosine function with a minimum point at $\left(\frac{\pi}{2}, -2\right)$ and a maximum point at $(\pi, 8)$. The function is of the form $$y

1. **Problem Statement:** We have two trigonometric functions given in the form $f(x) = a \sin[b(x - c)] + d$ and $y = a \cos[b(x - c)] + d$ with given maximum and minimum points.

1. **Problem Statement:** Calculate the inverse cosine (arccos) values and angles for given cosine values and right triangles. 2. **Formula and Rules:**