📏 trigonometry

1. Stating the problem: Find the exact values of the following trigonometric functions: (a) $\tan(\frac{\pi}{3})$

1. Convert degrees to radians. (a) Given $300^\circ$, use the formula $\text{radians} = \text{degrees} \times \frac{\pi}{180}$.

1. **Problem statement:** Prove the following identities:

1. Convert from degrees to radians: (a) The formula to convert degrees to radians is $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$.

1. **Prove** $\tan \theta \sin \theta + \cos \theta = \sec \theta$. Start from the left side (LHS):

1. **State the problem:** Jimmy is on a ship 708 meters away from the base of a cliff. The angle of elevation to the top of the lighthouse on the cliff is 26 degrees. We need to fi

1. Problem statement: Jimmy is on a ship 708 meters away from the base of a cliff. The angle of elevation from Jimmy to the top of the lighthouse on the cliff is $26^\circ$. 2. We

1. Stating the problem: We have a light post 5 m tall casting a shadow of 9.3 m. We need to find the angle of elevation of the sun at that time, denoted as $\theta$, rounded to two

1. **State the problem:** Eileen measures the angle of elevation to the top of a tree to be 42° from a point 27 metres away from the base. Find the height $h$ of the tree.

1. **Problem Statement:** Find the lengths of the sides labeled $y$ and $z$ in two right-angled triangles where each triangle has a given side length adjacent to a given angle.

1. **Problem (a):** Calculate the length of the side $w$, opposite the $15^\circ$ angle, in a right triangle with hypotenuse $10$ cm. 2. Use the sine function because sine relates

1. Let's clarify the problem: You have given two angle measures, 298° and 298.165°, and you mention two rectangles stacked vertically with quotation marks. The question seems uncle

1. The problem is to convert the angle 336° 44' 33'' to decimal degrees. 2. Recall that 1 degree ($1^\circ$) equals 60 minutes (') and 1 minute equals 60 seconds ('').

1. **State the problem:** We need to find the bearing of point U from point T given that the angle between the vertical line from T to N and the line from T to U is 76° to the left

1. To clarify your question, it seems you are asking about why the last function or expression involves the tangent function (tan). 2. The tangent function typically appears as the

1. Solve for $\Theta$ in the equation $\sin \Theta - \sec \Theta + \csc \Theta - \tan 20^\circ = -0.0866$. - Calculate $\tan 20^\circ \approx 0.36397$.

1. State the problem: Solve the equation $$\sin(x) - \sqrt{\pi} \cos(x) = 0$$ for $x$. 2. Rearrange the equation to isolate terms: $$\sin(x) = \sqrt{\pi} \cos(x)$$.

1. Stated problem: Simplify or analyze the expression $$\sin(x) - \sqrt{\pi} \cos(x).$$ 2. Understanding the expression: This is a linear combination of sine and cosine functions w

1. **State the problem:** We need to show that the equation $$\tan 2x = 5 \sin 2x$$ can be written as $$(1 - 5 \cos 2x) \sin 2x = 0$$ and then solve this equation for $0 \leq x \le

1. The problem asks to analyze the graph transformations for sine functions. 2. Part (a) asks the transformation mapping from $y=\sin x$ to $y=\sin 5x$.

1. **State the problem:** Simplify the expression $$(1+\cot A - \csc A)(1 + \tan A + \sec A)$$. 2. **Recall definitions:**