Which Set of Angles has the same Trigonometric Ratio?
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Updated Jun 17, 2024
Which Set of Angles has the same Trigonometric Ratio?
The given problem is to find which set of angles has the same trigonometric ratio.
- sin 45 and tan 45
- sin 30 and cos 60
- cos 30 and tan 45
- tan 60 and sin 45
Trigonometric ratios are functions of an angle used in various calculations involving right-angled triangles. The main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). These ratios have specific values for particular angles.
Key Trigonometric Ratios
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
Specific Angle Values
sin 45° = √2/2
tan 45° = 1
sin 30° = 1/2
cos 30° = √3/2
tan 30° = 1/√3
cos 60° = 1/2
tan 60° = √3
In the given the sets of angles
sin 30° = 1/2 and cos 60° = 1/2
These values are equal.
Among the given options, the set of angles that has the same trigonometric ratio is
sin 30° and cos 60°
Trigonometric Ratios and Properties
Trigonometric ratios are fundamental concepts in trigonometry, a branch of mathematics that deals with the relationships between the angles and sides of triangles. These ratios are especially important in right-angled triangles.
Trigonometric Ratios
Sine (sin):
The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the hypotenuse.
sin(θ) = opposite/hypotenuse
Cosine (cos):
The cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse.
cos(θ) = adjacent/hypotenuse
Tangent (tan):
The tangent of an angle is the ratio of the length of the opposite side to the adjacent side.
tan(θ) = opposite/adjacent
Applications
- Trigonometric ratios are used in various fields such as physics, engineering, and astronomy.
- They help in calculating distances and angles in navigation and surveying.
- In architecture and construction, trigonometric ratios assist in designing structures and ensuring stability.
- Trigonometric ratios and their properties are essential for solving problems involving right-angled triangles. These ratios provide a foundation for more advanced studies in mathematics and science.
