📏 trigonometry

1. The problem is to simplify the expression $$\frac{\cos A}{1-\tan A} + \frac{\sin A}{1-\cot A}$$. 2. Recall that $$\tan A = \frac{\sin A}{\cos A}$$ and $$\cot A = \frac{\cos A}{\

1. பிரச்சினையை விளக்குகிறோம்: \( \sin^{-1}\left(\frac{1}{10}\right) \) என்பதன் மதிப்பையும்,\nஇருப்பின் உள்ள அடிப்படையில் \( \frac{H}{u} - \frac{w}{10} \),\n\( 5u \), மற்றும் \( \fr

1. Solve for \( \Theta \) in the equation \( \sin \Theta - \sec \Theta + \csc \Theta - \tan 20^\circ = -0.0866 \). Given options: 40°, 41°, 47°, 43°. Calculate \( \tan 20^\circ \ap

1. State the problem: Solve the trigonometric equation $$\sin x = \frac{1}{2}$$ for $$x$$ in the interval $$[0, 2\pi]$$. 2. Recall that $$\sin x = \frac{1}{2}$$ at angles where $$x

1. **Multiple Choice Questions - Answers:** 1. The angle measured clockwise from north is called a **bearing**. Answer: c. Bearings

1. **State the problem:** Prove the identity $$\frac{\cos x}{\csc^2 x - 1} = \sin x \tan x$$

1. We are given the equation $\sqrt{3} \sin(x) - \cos(x) = 0$ and need to find the values of $x$ that satisfy it. 2. Rewrite the equation to isolate terms: $\sqrt{3} \sin(x) = \cos

1. Stating the problem: Prove that $$\frac{1 - \sin \theta}{\cos \theta} = \frac{\cos \theta}{1 + \sin \theta}$$. 2. Start with the left-hand side (L.H.S): $$\frac{1 - \sin \theta}

1. The problem is to plot graphs of trigonometric functions. 2. The main trigonometric functions to consider are sine ($y=\sin x$), cosine ($y=\cos x$), and tangent ($y=\tan x$).

1. The problem is to simplify the expression $\cos a - \cos b$. 2. Recall the cosine difference identity:

1. We want to find the formula for \(\sin a - \sin b\). 2. The sine subtraction formula is given by:

1. The problem asks for the domain and range of all trigonometric functions. 2. The primary trigonometric functions are sine ($\sin x$), cosine ($\cos x$), and tangent ($\tan x$).

1. The problem is to find the solutions for the equation $\sin x = \cos x$. 2. We know from trigonometry that $\sin x = \cos x$ means the sine and cosine values of the same angle a

1. **State the problem:** Find the exact formula for the function $g(x) = a \sin(bx + c) + d$ given that it has a minimum point at $(1, 1)$ and crosses its midline at $(1.5, 1.5)$.

1. প্রথম সমীকরণটি হল $2 \tan^2 x - y \tan x + 1 = 0$। এখানে চলরাশি (variable) হচ্ছে যেটি আলফাবেটিক্যালি লেখা আছে বা যা পরিবর্তনশীল হিসেবে বিবেচিত হচ্ছে।\n\n2. এখানে $y$ একটি অজানা

1. The problem asks to find the value of \( \sec \theta \) when \( 3\pi/2 < \theta < 2\pi \) and \( \sec \theta = \sqrt{5} \). 2. Recall that \( \sec \theta = \frac{1}{\cos \theta}

1. The problem asks to identify the 5 points that belong to the graph of the function $$g(x) = 3\sin(2x) - 2$$ from given points on the grid. 2. We start by evaluating $$g(x)$$ at

1. Problem a: Find the new coordinates of point P after the transformation from $y=\tan x$ to $y=\tan 5x$. - Given original point $P=(45^\circ,1)$ on $y = \tan x$.

1. Stating the problem: Prove the identity $$\csc 2A = \frac{1}{2}(\sec A \csc A)$$. 2. Recall the double angle identity for cosecant: $$\csc 2A = \frac{1}{\sin 2A}$$.

1. **State the problem:** We are given a trigonometric function of the form $$g(x) = a \sin(bx + c) + d$$. We know two points: the function crosses its midline at (1.5, 1.5) and ha

1. The problem is to convert the angle \(\theta = 310^\circ\) from degrees to radians. 2. Recall the conversion formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).