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Questions and Answers
What is the sine of the angle in a right-angled triangle?
What is the sine of the angle in a right-angled triangle?
- Adjacent/Hypotenuse
- Opposite/Hypotenuse (correct)
- Opposite/Adjacent
- Hypotenuse/Opposite
What is the tangent of the angle in a right-angled triangle?
What is the tangent of the angle in a right-angled triangle?
- Opposite/Adjacent (correct)
- Adjacent/Opposite
- Opposite/Hypotenuse
- Hypotenuse/Opposite
What is the cosine of the angle in a right-angled triangle?
What is the cosine of the angle in a right-angled triangle?
- Hypotenuse/Opposite
- Opposite/Adjacent
- Adjacent/Hypotenuse (correct)
- Opposite/Hypotenuse
What is the Pythagorean theorem used for?
What is the Pythagorean theorem used for?
In a right-angled triangle, what is the ratio of the side opposite the angle to the hypotenuse?
In a right-angled triangle, what is the ratio of the side opposite the angle to the hypotenuse?
What is the ratio of the side adjacent to the angle to the hypotenuse in a right-angled triangle?
What is the ratio of the side adjacent to the angle to the hypotenuse in a right-angled triangle?
Which trigonometric ratio represents the ratio of the side opposite the angle to the side adjacent to the angle in a right-angled triangle?
Which trigonometric ratio represents the ratio of the side opposite the angle to the side adjacent to the angle in a right-angled triangle?
What is the reciprocal of sine in a right-angled triangle?
What is the reciprocal of sine in a right-angled triangle?
What is the relationship between the cosine and sine of an angle in a right-angled triangle?
What is the relationship between the cosine and sine of an angle in a right-angled triangle?
In a right-angled triangle, if the sine of an angle is $\frac{3}{5}$, what is the cosine of the same angle?
In a right-angled triangle, if the sine of an angle is $\frac{3}{5}$, what is the cosine of the same angle?
What is the value of the tangent of an angle in a right-angled triangle if the side opposite the angle is 7 and the side adjacent to the angle is 24?
What is the value of the tangent of an angle in a right-angled triangle if the side opposite the angle is 7 and the side adjacent to the angle is 24?
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Study Notes
Trigonometric Ratios in Right-Angled Triangles
- Sine (sin) of an angle: Ratio of the length of the opposite side to the hypotenuse.
- Cosine (cos) of an angle: Ratio of the length of the adjacent side to the hypotenuse.
- Tangent (tan) of an angle: Ratio of the length of the opposite side to the length of the adjacent side.
Pythagorean Theorem
- Used to relate the lengths of the sides of a right-angled triangle: ( a^2 + b^2 = c^2 ), where ( c ) is the hypotenuse.
Ratios in Right-Angled Triangles
- Opposite/Hypotenuse gives the sine of the angle.
- Adjacent/Hypotenuse gives the cosine of the angle.
- Opposite/Adjacent gives the tangent of the angle.
Reciprocal Relationships
- The reciprocal of sine is cosecant (csc).
- The relationship between cosine and sine for an angle ( \theta ): ( \cos(θ) = \sqrt{1 - \sin^2(θ)} ).
Example Calculations
- If ( \sin(θ) = \frac{3}{5} ), then the cosine can be calculated using ( \cos(θ) = \sqrt{1 - (\frac{3}{5})^2} = \frac{4}{5} ).
- To find the tangent of an angle where the opposite side is 7 and the adjacent side is 24, calculate ( \tan(θ) = \frac{7}{24} ).
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