# Component

## Component: Trigonometric ratios

### Question 2

Written Paper Section I Question 2 - 2002 HSC

Find the equation of a tangent to a curve. Differentiate and integrate functions. Use the sine rule to find the exact value of a ratio.

### Question 3

Written Paper Section I Question 3 - 2001 HSC

Evaluate a definite integral. Find the value of a constant in a formula and apply the formula. Differentiate functions. Verify a given equation for a triangle by using the cosine rule, and hence an unknown side-length of the triangle.

### Question 4

Written Paper Section I Question 4 - 2002 HSC

Solve and graph an absolute value inequation. Solve a simple trigonometric equation for a specified range. Calculate the length of a side and the area of a given triangle. Show that a given pair of coordinates represents the point of intersection of two curves. Find the size of the shaded area bounded by the two curves.

### Question 5

Written Paper Section I Question 5 - 2010 HSC

Show that the surface area of a cylinder has a minimum value for a particular value of its radius. Prove trigonometric identities and find the exact value of an integral. Find the ordinates at two x-values for areas under a curve enclosed by the x-axis, a given ordinate and the ordinates to be found, and the curve.

### Question 9

Written Paper Section I Question 9 - 2001 HSC

Verify the size of a specified angle and hence that two triangles within the given diagram are similar. Deduce an equation. Use the cosine rule to deduce the exact value of the cosine ratio of angles within the given diagram. Given an expression for the time rate of change of a quantity, find the initial rate. Find an expression for a volume. Verify and solve a given equation for a particular value of the volume.

### Question 10

Written Paper Section I Question 10 - 2010 HSC

Show two specified triangles are similar. Show relationships involving the side lengths of the similar triangles. Find an expression for the volume of a solid of revolution. Apply the expression found in solving a problem involving a hemispherical container.

### Question 10

Written Paper Section I Question 10 - 2001 HSC

Apply geometric series concepts to financial situations. Find two expressions to describe travel situations and use the expressions to solve a real-world problem.