17 27 520 17 In the figure above, sin 52° Based on the figure, which of the following equations is also true? C A sin 38° 17 17 cos 38° = C 17 C cos 52° -
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![**Trigonometry Problem: Finding the Correct Equation**
**Question 27/36**
In the figure below, we see a right triangle. The angle labeled \(52^\circ\) is opposite the side labeled 17, and \(c\) is the hypotenuse of the triangle. The sine of 52 degrees (\(\sin 52^\circ\)) is given by the ratio of the opposite side to the hypotenuse:
\[ \sin 52^\circ = \frac{17}{c} \]
The task is to determine which of the following equations is also true based on the given figure:
(A) \( \sin 38^\circ = \frac{c}{17} \)
(B) \( \cos 38^\circ = \frac{17}{c} \)
(C) \( \cos 52^\circ = \frac{17}{c} \)
(D) \( \tan 52^\circ = \frac{c}{17} \)
### Figure Explanation:
The provided diagram is a right triangle:
- One angle is labeled \(52^\circ\).
- The side opposite the \(52^\circ\) angle is of length 17.
- The hypotenuse is labeled as \(c\).
### Solution Steps:
1. **Understanding Trigonometric Ratios:**
- For angle \(52^\circ\):
\[ \sin 52^\circ = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{17}{c} \]
2. **Analyzing the Options:**
- **Option A: \( \sin 38^\circ = \frac{c}{17} \)**
According to trigonometric identities, \( \sin \theta = \cos (90^\circ - \theta) \). Here, \( \sin 38^\circ \) would also consider the other sides of the triangle.
- **Option B: \( \cos 38^\circ = \frac{17}{c} \)**
This could be true if we consider the complementary angle property: \( 38^\circ = 90^\circ - 52^\circ \). Hence, \( \cos 38^\circ = \sin 52^\circ \).
- **Option C: \( \cos 52^\circ = \frac{17}{c} \)**
This would be incorrect as \( \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34bff1e1-af68-4229-b0ef-aa0aaa134e46%2F2a0878b9-64c5-45f3-863d-3708ee1cd97c%2Fedrqott_processed.jpeg&w=3840&q=75)
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