📏 trigonometry

1. **Problem Statement:** Find the exact values of the following trigonometric functions: (a) $\tan\left(\frac{\pi}{3}\right)$

1. The problem is to find an angle in a triangle using the sine rule. 2. The sine rule formula is $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, $c$ are

1. The problem is to clarify whether the formula gives the length of the opposite side or the opposite angle in a triangle. 2. The sine rule formula $\frac{a}{\sin A} = \frac{b}{\s

1. **Problem Statement:** Find the exact values of the following trigonometric functions: (a) $\tan\left(\frac{\pi}{3}\right)$

1. The problem is to find where 120 degrees falls on the unit circle or in radians. 2. First, convert 120 degrees to radians using the formula $\text{radians} = \text{degrees} \tim

1. The problem is to convert 1000 degrees to radians. 2. The formula to convert degrees to radians is $\text{radians} = \text{degrees} \times \frac{\pi}{180}$.

1. The problem is to convert 1000 degrees to radians. 2. The formula to convert degrees to radians is $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$.

1. The problem is to convert 1000 degrees to radians. 2. The formula to convert degrees to radians is $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$.

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

1. Convert from degrees to radians. The formula to convert degrees to radians is:

1. **Problem Statement:** Find the exact values of the following trigonometric functions: (a) $\tan\left(\frac{\pi}{3}\right)$

1. **Stating the problem:** We are given the complex number with argument $\text{Arg } Z = -\pi$ and real part $\text{Re } Z = -1$, and we want to evaluate $\cos^4 x$ for some $x$.

1. **State the problem:** We need to find the length $f$ in a right triangle where one angle is $38^\circ$, the adjacent side to this angle is $7.2$ cm, and $f$ is the side opposit

1. The problem is to prove the identity $$\frac{\tan 4A - \tan 3A}{1 + \tan 4A \tan 3A} = \tan A.$$\n\n2. Recall the tangent subtraction formula: $$\tan(x - y) = \frac{\tan x - \ta

1. **Problem Statement:** We need to understand why the period of a sinusoidal function with given characteristics is 8 and not 4.

1. Let's start by understanding what a period means in the context of functions, especially trigonometric functions like sine and cosine. 2. The period of a function is the length

1. **Problem Statement:** We analyze the height function of a Ferris wheel over time, which is sinusoidal and periodic. 2. **Periodicity:** A function is periodic if it repeats its

1. **State the problem:** We need to sketch a sinusoidal function with period 8, amplitude 5, axis at $y=-1$, and 2 cycles.

1. **State the problem:** We need to sketch a sinusoidal function with period 8, amplitude 5, axis at $y=-1$, and 2 cycles.

1. **State the problem:** We are given a sinusoidal function with period 8, amplitude 5, axis at $y=-1$, and 2 cycles shown. We want to write the equation of this sinusoidal functi

1. **State the problem:** We need to sketch a sinusoidal function with period 8, amplitude 5, axis at $y=-1$, and 2 full cycles.