Trigonometry

1. (a) The diagram shows the graph and a line parallel to the -axis.

Given that one point of intersection is when , write down the values of and C .

(b) The diagram shows the graph and a line parallel to the -axis.

Given that one point of intersection is when , write down the values of P and Q.

2. In this question you must show detailed reasoning.
is an obtuse angle and . Work out the exact values of and .
3. You are given that the equation has solution . Write down all the values of in the range
(a) satisfying the equation
(b) satisfying the equation
satisfying the equation
4. Yahya is attempting to prove the cosine rule for the triangle shown below. He starts by adding the dotted lines as shown.

Here are the first few lines of his proof.

Complete his proof explaining clearly what you have done.
5. Find the perimeter and area of the triangle shown below.
6. Marisa is on a Ferris wheel, watched by her friend Tash who is directly below the wheel as shown in the diagram. Tash looks up and sees Marisa’s capsule directly overhead in position . Exactly 150 seconds later Marisa’s capsule is directly overhead again in position . The Ferris wheel turns anticlockwise as shown by the arrow.

Given that the Ferris wheel has radius 15 m and is going at a constant speed and that Tash is a horizontal distance of 9 m from the lowest point of the wheel, work out how long the Ferris wheel takes to make one full revolution.

7. In this question you must show detailed reasoning.

Solve these equations for .
(a)
(b)

8. In this question you must show detailed reasoning.

The diagram shows parts of the curves and where is in degrees.
Solve the inequality for .