📏 trigonometry

1. The problem states that $\cot \theta = \frac{\sqrt{3}}{2}$. We need to find $\theta$ or related trigonometric values. 2. Recall that $\cot \theta = \frac{\cos \theta}{\sin \thet

1. **State the problem:** Given that $\sec \theta = 3$, find the values of $\cos \theta$ and $\sin \theta$. 2. **Recall the definition:** $\sec \theta = \frac{1}{\cos \theta}$.

1. **State the problem:** We need to fill in the missing values in the table for the function $y = -\sec(x)$ at $x = 0.1$ and $x = 0.2$ to 3 decimal places. 2. **Recall the functio

1. The problem asks us to find the values of $y = \cos(x)$ for the given $x$ values: $-1$, $-\frac{2}{3}$, $-\frac{1}{3}$, $0$, $\frac{1}{3}$, $\frac{2}{3}$, and $1$. We will calcu

1. **State the problem:** We need to find the length $f$, which is the height of a right triangle opposite the $38^\circ$ angle. The base adjacent to this angle measures 7.2 cm. 2.

1. The problem is to determine if the function $\sin(x)$ is bijective. 2. A function is bijective if it is both injective (one-to-one) and surjective (onto).

1. The problem is to understand the function $\sin(x)$ and its properties. 2. The sine function, $\sin(x)$, is a periodic function with period $2\pi$, meaning $\sin(x + 2\pi) = \si

1. **State the problem:** Simplify the expression $$\frac{1 + \sin u}{\cos u} + \frac{\cos u}{1 + \sin u}$$. 2. **Find a common denominator:** The common denominator is $$\cos u (1

1. **State the problem:** We have a triangle with angles 70° and 61°, and the side opposite the 61° angle is 15 units. We need to find the side length opposite the 70° angle using

1. **State the problem:** We are given a triangle with angles 118°, 28°, and the remaining angle, and a side length of 5 opposite the 28° angle. We need to find the side length opp

1. **State the problem:** We are given a triangle with angles 25° and 96°, and the side opposite the 25° angle is 13 units. We need to find the length of the side opposite the 96°

1. Problem 4.1: Prove without using a calculator that $\sin 44^\circ + \sin 16^\circ = \sin 76^\circ$. Use the sum-to-product identity $\sin A + \sin B = 2\sin\frac{A+B}{2}\cos\fra

1. **State the problem:** Prove the trigonometric identity $$\tan \theta + \cot \theta \equiv \frac{2}{\sin 2\theta}$$. 2. **Recall definitions:**

1. Let's start by stating the problem: We want to understand and derive the fundamental trigonometric equations related to triangles. 2. Consider a right triangle with an angle $\t

1. Convert from degrees to radians. (a) To convert 300° to radians, use the formula $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$.

1. Problem 9: Calculate the wingspan (length of segment DC) of the Wawa Goose given points A and B 4m apart, angles \(\angle BAC = 29^\circ\), \(\angle DAB = 81^\circ\), and \(\ang

1. Prove (a) $\cos x \tan^3 x = \sin x \tan^2 x$. Step 1: Recall that $\tan x = \frac{\sin x}{\cos x}$.

1. **State the problem:** Solve the equation $$2 \cos^2 x - 3 \sin x = 3$$ for $$0 \leq x \leq 2\pi$$. 2. **Rewrite the equation using the Pythagorean identity:** Recall that $$\co

1. The problem states: Given $\cos a = \frac{5}{7}$ and the terminal side of angle $a$ lies in a certain quadrant, find the quadrant and evaluate $\cos\left(-\frac{a}{2}\right)$ us

1. **State the problem:** Autumn spots a plane flying at a constant altitude of 6950 feet. She measures the angle of elevation to the plane as 15° at point A and later as 38° at po

1. **State the problem:** Autumn spots a plane flying at a constant altitude of 69506950 feet. She measures the angle of elevation to the plane as 15° at point A and later as 38° a