11 Questions
What is the sine of the angle in a right-angled triangle?
Opposite/Hypotenuse
What is the tangent of the angle in a right-angled triangle?
Opposite/Adjacent
What is the cosine of the angle in a right-angled triangle?
Adjacent/Hypotenuse
What is the Pythagorean theorem used for?
Finding the relationship between sides in a right-angled triangle
In a right-angled triangle, what is the ratio of the side opposite the angle to the hypotenuse?
Sine
What is the ratio of the side adjacent to the angle to the hypotenuse in a right-angled triangle?
Cosine
Which trigonometric ratio represents the ratio of the side opposite the angle to the side adjacent to the angle in a right-angled triangle?
Tangent
What is the reciprocal of sine in a right-angled triangle?
Cosecant
What is the relationship between the cosine and sine of an angle in a right-angled triangle?
The cosine of an angle is the reciprocal of the sine of the same 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?
$\frac{4}{5}$
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?
$\frac{7}{24}$
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} ).
Test your knowledge of basic trigonometry concepts with this quiz. Answer questions about sine, cosine, tangent, and the Pythagorean theorem in right-angled triangles.
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