QuestionThe cosine function for a specific angle in a triangle is defined by the ratio of the triangle's A) opposite side and adjacent side. B) adjacent side and opposite angle. C) opposite side and hypotenuse. D) adjacent side and hypotenuse.
Studdy Solution
STEP 1
1. We are dealing with a right triangle.
2. The cosine function is a trigonometric function that relates the angle of a right triangle to the lengths of its sides.
STEP 2
1. Recall the definition of the cosine function.
2. Identify the sides of the triangle relevant to the cosine function.
3. Match the definition to the given options.
STEP 3
Recall the definition of the cosine function in the context of a right triangle. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
STEP 4
Identify the sides of the triangle relevant to the cosine function. In a right triangle: - The "adjacent side" is the side next to the angle of interest, excluding the hypotenuse. - The "hypotenuse" is the longest side of the triangle, opposite the right angle.
STEP 5
Match the definition to the given options:
- Option A: opposite side and adjacent side (incorrect, this is the tangent function).
- Option B: adjacent side and opposite angle (incorrect, angles are not sides).
- Option C: opposite side and hypotenuse (incorrect, this is the sine function).
- Option D: adjacent side and hypotenuse (correct, this matches the definition of cosine).
The correct answer is .
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