📏 trigonometry

1. **State the problem:** We need to write sine and cosine functions for a curve with given parameters: midline $-1$, amplitude $2$, and horizontal shift left by $\frac{\pi}{4}$. T

1. **Énoncé du problème :** Nous travaillons dans un plan muni d'un repère orthonormé direct (O, I, J).

1. Hisoblang: $$\frac{\sin 36^{0}}{\sin 12^{0}} \cdot \frac{\cos 36^{0}}{\cos 12^{0}}$$ Formula: Use exact values or known trigonometric identities.

1. The problem is to find the expression for $\sin 2x$. 2. We use the double-angle formula for sine: $$\sin 2x = 2 \sin x \cos x$$.

1. The problem is to find $\tan A$ given an angle $A$. 2. Recall the definition of tangent in a right triangle: $\tan A = \frac{\text{opposite}}{\text{adjacent}}$.

1. Prove (cosec \theta - cot \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}. Start with the left-hand side (LHS):

1. **State the problem:** We need to analyze the function $f(x) = \sin(x + \pi)$ to find its periodic time (period) and points of intersection with the horizontal axis and the edge

1. The problem asks to find the period and points of intersection with the horizontal axis (x-intercepts) for the given trigonometric functions. 2. Recall the period formulas for s

1. **Problem statement:** From a point on the ground, the angle of elevation to a skyscraper 500 metres away is 15°. 2. **Formula and rules:** To find the height $h$ of the skyscra

1. **State the problem:** Verify the identity:

1. **State the problem:** Prove or verify the identity:

1. **State the problem:** Prove that $$\cos A - \sin A + 1 = \csc A + \cot A$$ using the identity $$\csc^2 A = 1 + \cot^2 A$$. 2. **Recall the identity:** We know that $$\csc^2 A =

1. **State the problem:** Prove the identity $$\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \csc \theta$$

1. **Problem statement:** An aeroplane flies from Lilongwe on a bearing of 031° for 20 km, then changes course and flies 140 km on a bearing of 074°. Find: a) The distance of Lilon

1. **Problem Statement:** Find the related acute angle for the angle 135° in standard position.

1. **State the problem:** We have a right-angled triangle with one angle of 28 degrees and the side adjacent to this angle measuring 12 meters. We need to find the hypotenuse. 2. *

1. **State the problem:** We want to find the number of solutions to the equation $$|2 + 3 \sin 2x| = 1$$. 2. **Understand the absolute value equation:** The equation $$|A| = B$$ m

1. **State the problem:** We are given a right triangle TUV with a right angle at V. The side opposite angle V is 8 units, the hypotenuse is 15 units, and the side adjacent to angl

1. **State the problem:** We need to determine which of the two acute angles in a right triangle has a cosine value of $\frac{4}{5}$. The triangle has sides $AB=6$, $BC=8$, and hyp

1. **State the problem:** We need to find the angle $\theta$ in the triangle formed by the sides 3 m, 4 m, and 5.5 m, where $\theta$ is the angle between the 4 m and 3 m sides. 2.

1. **Problem statement:** We need to find the height of a tower given that the angle of elevation from the top of a 5 m high building to the top of the tower is 30 degrees, and the