Trigonometric Functions for Grade 10

Define sine, cosine, and tangent functions.

• Sine, cosine, and tangent functions are applicable only to obtuse angles.

• Sine, cosine, and tangent functions are used in algebraic equations only.

• Sine, cosine, and tangent functions relate angles of a right triangle to the lengths of its sides.

• Sine, cosine, and tangent functions are used to calculate the area of a circle.

Explain how to find the sine, cosine, and tangent of an angle in a right triangle.

• Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent

• Sine = Adjacent / Opposite, Cosine = Hypotenuse / Opposite, Tangent = Adjacent / Hypotenuse

• Sine = Adjacent / Hypotenuse, Cosine = Opposite / Hypotenuse, Tangent = Adjacent / Opposite

• Sine = Hypotenuse / Opposite, Cosine = Hypotenuse / Adjacent, Tangent = Opposite / Adjacent

What are the primary trigonometric ratios?

• sine, cosine, tangent

• cotangent

• secant

• cosecant

Discuss the reciprocal trigonometric ratios.

• The reciprocal trigonometric ratios are the hypotenuse, adjacent, and opposite sides of a right triangle.

• Reciprocal trigonometric ratios involve the angles of a triangle.

• Reciprocal trigonometric ratios are the cosecant (csc), secant (sec), and cotangent (cot) functions, which are the reciprocals of sine, cosine, and tangent respectively.

• Reciprocal trigonometric ratios are the tangent, cosine, and sine functions.

How are trigonometric functions used in real-life applications?

• Trigonometric functions are primarily used in literature to analyze poetic structures.

• Trigonometric functions are used in cooking recipes to determine ingredient ratios.

• Trigonometric functions are only used in theoretical mathematics and have no practical applications.

• Trigonometric functions are used in real-life applications such as architecture, engineering, physics, and navigation to model periodic phenomena like sound waves, light waves, and oscillations. They help in calculating angles, distances, and heights in various practical scenarios.

Solve for unknown sides and angles using trigonometric functions.

• Calculate the area of a circle

• Solve a system of linear equations

• JSON output with the calculated unknown sides and angles

• Find the square root of a number

What is the unit circle and its significance in trigonometry?

• The unit circle is a line segment with endpoints at (0,1) and (0,-1) used in geometry.

• The unit circle is a square used to calculate tangent and cotangent functions.

• The unit circle is a triangle with sides of length 2 used in calculus.

• The unit circle is a circle with a radius of 1 centered at the origin, used to define sine and cosine functions in trigonometry.

Explain the concept of periodicity in trigonometric functions.

• Periodicity in trigonometric functions means the function values never repeat

• Periodicity in trigonometric functions is the property where the function values repeat at regular intervals. For example, sine and cosine functions have a periodicity of 2π, meaning their values repeat every 2π radians.

• Trigonometric functions have a periodicity of 3π

• Periodicity in trigonometric functions refers to the number of asymptotes in the graph

Discuss the relationship between trigonometric functions and the Pythagorean theorem.

• Trigonometric functions are not related to the Pythagorean theorem

• The Pythagorean theorem does not involve right triangles, unlike trigonometric functions

• The Pythagorean theorem only applies to acute angles, not trigonometric functions

• The trigonometric functions sine and cosine are defined in terms of the sides of a right triangle, which is a fundamental concept in the Pythagorean theorem.

How do you graph trigonometric functions?

• Guess the shape without any calculations

• Connect points randomly to form the graph

• Use random points to plot the graph

• Identify parameters, plot key points, and connect them to form the graph.