Trigonometry Basics Quiz

What is the sine of the angle in a right-angled triangle?

What is the tangent of the angle in a right-angled triangle?

What is the cosine of the angle in a right-angled triangle?

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?

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?

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?

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?

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.