📏 trigonometry

1. The problem is to convert an angle from degrees to radians. 2. The formula to convert degrees to radians is:

1. **State the problem:** Simplify the expression $$y = \frac{\sin 2x}{\sin x}$$ and understand its behavior. 2. **Recall the double-angle formula for sine:** $$\sin 2x = 2 \sin x

1. **State the problem:** Simplify the expression $$y = \frac{1 - \sec^2(5x^2)}{\cot(5x^2)}$$. 2. **Recall relevant identities:**

1. The problem is to calculate the value of $\cos 40^\circ \times \sin 60^\circ$. 2. Recall the values and properties:

1. **State the problem:** Simplify the expression $\cos A + \sin A$. 2. **Recall the formula:** There is no direct simplification for $\cos A + \sin A$ alone, but it can be express

1. The problem is to simplify the expression \( \cos a + \sin a \). 2. There is no direct simplification formula for \( \cos a + \sin a \) alone, but it can be expressed as a singl

1. **State the problem:** We need to find an equation for the graph that decreases sharply from the top-left, passes through the origin near $\left(\frac{3\pi}{4},0\right)$, and go

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. The problem is to understand the expression \(\sin 5x\) and \(\sin^5 x\) and how they differ. 2. \(\sin 5x\) means the sine of \(5x\), which is the sine function applied to the

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

1. The problem is to find the value of \(\sin(2\theta)\) given a trigonometric context. 2. The double-angle formula for sine is \(\sin(2\theta) = 2\sin(\theta)\cos(\theta)\).

1. **Problem Statement:** We need to find the equation of the trigonometric function shown in the graph. 2. **Observations from the graph:**

1. **State the problem:** We need to find angle $A$ in a right triangle where side $a = 103.3$ cm, side $b = 152.5$ cm, and angle $C = 90^\circ$. 2. **Recall the ABCabc format:** I

1. **State the problem:** We need to find the hypotenuse $c$ of a right triangle where side $a = 64.1$ cm and angle $B = 58.2^\circ$. The triangle is labeled such that $C = 90^\cir

1. Let's solve a problem involving trigonometry. 2. Suppose we want to find the value of $\sin(30^\circ)$.

1. **Problem:** Given $\tan \theta + \frac{1}{\tan \theta} = 2$, find the value of $\tan^2 \theta + \frac{1}{\tan^2 \theta}$. **Step 1:** Let $x = \tan \theta$. Then the equation b

1. **State the problem:** Find the exact values of $\sin 15^\circ$ and $\cos 105^\circ$.\n\n2. **Recall formulas:** Use the angle difference and sum identities:\n\n$$\sin(a - b) =

1. **Problem Statement:** We need to find the distance of an aircraft from point K on the horizontal ground given the angle of elevation. 2. **Understanding the Problem:** The angl

1. **Problem statement:** We need to find the distance of an aircraft from a point K on the horizontal ground given the angle of elevation. 2. **Understanding the problem:** The an

1. समस्या: यदि $\cos a = -\frac{4}{5}$ र कोण $a$ दोस्रो चतुर्थांशमा पर्छ भने, $\sin a$ को मान पत्ता लगाउनुहोस्। त्यसपछि $\frac{1 + \sin a}{1 - \cos a}$ को मान निकाल्नुहोस्। 2. सूत्