📏 trigonometry

1. **Problem a:** Solve $$3 \tan^2 y - 2 \sec y - 2 = 0$$ for $$0^\circ \leq y \leq 360^\circ$$. 2. Recall the identities: $$\sec y = \frac{1}{\cos y}$$ and $$\tan^2 y = \sec^2 y -

1. **State the problem:** Prove or simplify the expression $$\sqrt{\frac{1 + \tan^2 A}{1 + \cot^2 A}} = \tan A$$. 2. **Recall the Pythagorean identities:**

1. The problem asks: In which quadrant does the terminal side of a $-45^\circ$ angle in standard position lie? 2. Recall that angles in standard position start from the positive x-

1. The problem asks: In which quadrant does the terminal side of a $-45^\circ$ angle in standard position lie? 2. Recall that angles in standard position start from the positive x-

1. **Problem Statement:** We have a right triangle RST with a right angle at S. Side RT (hypotenuse) is 35, side TS is 21, and we want to determine if each expression can find the

1. **State the problem:** Emma is 10 feet from the base of a tree and estimates the angle of elevation to the top is between 55° and 75°. We want to check if given height estimates

1. **State the problem:** We need to find the range of the function $$g(x) = 4\sin\left(0.5(x+30)\right) - 5$$. 2. **Recall the range of sine function:** The sine function $$\sin(\

1. **Problem statement:** Two planes are at the same altitude. One plane is 100 km away at direction N60°E, and the other is 160 km away at direction S50°E. We need to find the dis

1. **Problem statement:** Two planes are at the same altitude. One is 100 km away at direction N60°E, the other 160 km away at S50°E. We need to find the distance between the two p

1. **Problem Statement:** A dragon at point D breathes fire at point H with an angle of elevation of 33°. The target H is 11 cm below the dragon's horizontal eye level. A human at

1. **Problem Statement:** A dragon at point D breathes fire at a target H located 11 cm below its horizontal eye level, with an angle of elevation of 33° from D to H. A human at po

1. **Énoncé du problème :** Nous avons la fonction $d(t) = 10 \sin\left(\frac{19\pi}{6}(t - c)\right) + 15$ qui modélise la distance entre un papillon et un chat.

1. **Problem statement:** Given that angle $\theta$ terminates in the fourth quadrant and $\cos \theta = \frac{2}{5}$, find the exact value of $\tan \theta$. 2. **Recall the Pythag

1. **State the problem:** We have a right triangle with a 50° angle and hypotenuse length 8. We need to find the length of side $a$, which is opposite the 50° angle. 2. **Formula u

1. **Problem Statement:** We are given a triangle with one unknown side length and two unknown angles. We need to find the unknown side length rounded to the nearest tenth and the

1. The problem is to understand the cosine function, denoted as $\cos(x)$.\n\n2. The cosine function is a fundamental trigonometric function defined as the ratio of the adjacent si

1. The problem asks to find the angle from the equation previously solved. 2. To find an angle from an equation involving trigonometric functions, we typically use inverse trigonom

1. **Problem 1: Find the period of the pendulum ride given by** $$P(t) = -10 \sin\left(\frac{\pi}{3} t\right)$$ 2. The general form of a sine function is $$y = A \sin(Bt)$$ where t

1. Masalah yang diberikan adalah menyelesaikan persamaan trigonometri: $$2\cos^2 x - 1 = 0$$

1. The problem is to understand and solve a basic trigonometry question. 2. Trigonometry deals with the relationships between the angles and sides of triangles, especially right tr

1. Let's start by stating the problem: We want to understand why the graphs of $\sec x$ and $\csc x$ are different even though they seem similar. 2. Recall the definitions: