📏 trigonometry

1. **Problem Statement:** We need to find the angle created when the terminal point is located at the positive y-axis in a unit circle. 2. **Understanding the Unit Circle:** The un

1. **Problem statement:** In a right triangle, we are given that $\sin \theta = \cos \theta$. We need to find the value of $\tan \theta$. 2. **Recall the definitions:**

1. **Problem Statement:** Find the exact value of $\sin\left(-\frac{2\pi}{6}\right)$. 2. **Recall the sine function property:** $\sin(-x) = -\sin(x)$. This means the sine of a nega

1. The problem asks for the definition of the cosine of an angle in a right triangle. 2. In trigonometry, the cosine of an angle in a right triangle is defined as the ratio of the

1. The problem asks which formula correctly finds coterminal angles. 2. Coterminal angles are angles that differ by full rotations of 360 degrees.

1. **Stating the problem:** Given an angle $\theta$, can we find the largest and smallest angle coterminal with it? We need to understand the nature of coterminal angles. 2. **Defi

1. **State the problem:** Find the angle between $0$ and $2\pi$ that is coterminal with $-\frac{5\pi}{6}$.\n\n2. **Recall the concept:** Two angles are coterminal if they differ by

1. The problem asks to convert angles given in radians to degrees without using a calculator. 2. Recall the conversion formula between radians and degrees:

1. **Convert -0.69° to radians.** The formula to convert degrees to radians is:

1. **Problem Statement:** Find the reference angle for the given angles $\theta = 334^\circ$ and $\theta = 235^\circ$. 2. **Formula and Rules:**

1. **State the problem:** Determine the quadrant of the angle given in radians. 2. **Recall the quadrant rules for angles in radians:**

1. **Problem statement:** We have a right triangle with a hypotenuse of length 10, an angle of 30°, and the side adjacent to the 30° angle labeled as $5\sqrt{3}$. We need to find t

1. **Problem statement:** We have a right triangle with a 60° angle. The side opposite the 60° angle is $10\sqrt{3}$, the hypotenuse is 20, and the side adjacent to the 60° angle i

1. **State the problem:** Express $\sqrt{2} \cos x - \sqrt{5} \sin x$ in the form $R \cos(x + \alpha)$ where $R > 0$ and $0^\circ < \alpha < 90^\circ$. Then solve $\sqrt{2} \cos 2\

1. **State the problem:** We have a right triangle with hypotenuse 9.5 cm and adjacent side to angle $x$ equal to 8.3 cm. We need to find the angle $x$ in degrees, correct to 1 dec

1. The problem is to find the value of $\tan 90^\circ$. 2. Recall that the tangent function is defined as $\tan \theta = \frac{\sin \theta}{\cos \theta}$.

1. **Problem statement:** We have two points 25 km apart east-west. A ship sails 20 km from the first point on a bearing of 045°. We need to find the bearing of the second point fr

1. **State the problem:** Town A is 30 km north of town B. A ship sails 25 km from town A on a bearing of 120°. We need to find how far east and south the ship is from town B.

1. **State the problem:** Town A is 30 km north of town B. A ship sails 25 km from town A on a bearing of 120°. We need to find how far east and south the ship is from town B.

1. **State the problem:** Town A is 30 km north of town B. A ship sails 25 km from town A on a bearing of 120°. We need to find how far east and south the ship is from town B.

1. **Problem:** Given the equation $$\frac{\sin^2 x}{\cos x} - \frac{\sin^2 x}{1+\cos x} = 1$$ for $$0^\circ \leq x \leq 360^\circ$$, find the value(s) of $$x$$. 2. **Formula and r