Math Problem Statement
Solution
Let's solve this step by step.
Problem Summary:
We are tasked with finding the six trigonometric ratios for the angle in the triangle, where:
- (adjacent side to ),
- (opposite side to ).
Step 1: Find the hypotenuse using the Pythagorean theorem:
So, the hypotenuse .
Step 2: Write the trigonometric ratios:
-
Sine ():
-
Cosine ():
-
Tangent ():
-
Cosecant ():
-
Secant ():
-
Cotangent ():
Final Answer:
The six trigonometric ratios are:
Let me know if you'd like a more detailed breakdown!
Related Questions:
- What are the reciprocal relationships between trigonometric functions?
- How does the Pythagorean theorem relate to the unit circle?
- How do you find angles in degrees or radians from given trigonometric ratios?
- What happens to the trigonometric ratios if the triangle's sides are scaled up or down?
- How do you use these ratios in solving word problems or real-world scenarios?
Tip:
Memorizing the common right triangle ratios (e.g., 3-4-5, 5-12-13) can help speed up calculations without needing the Pythagorean theorem every time.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Formulas
Pythagorean theorem: c = √(a^2 + b^2)
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
csc θ = hypotenuse / opposite
sec θ = hypotenuse / adjacent
cot θ = adjacent / opposite
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 9-10