Trigonometry

You will be able to

• Calculate the hypotenuse of a right-angled triangle using c² = a² + b², giving the answer exactly as a surd or to 3 significant figures.
• Calculate a shorter side by subtracting the squares: a² = c² − b².
• Determine whether a triangle with three given sides is right-angled by checking whether a² + b² = c² for the longest side c.

You will be able to

• Identify the opposite, adjacent and hypotenuse relative to a given angle, and explain why opposite and adjacent swap for the other acute angle.
• Calculate a missing side or angle in a right-angled triangle using sine, cosine or tangent and their inverses, angles to 1 decimal place.
• Solve problems with angles of elevation and depression, measuring each angle from the horizontal.

You will be able to

• Choose between the sine rule and the cosine rule from the information given, and use them to calculate a missing side or angle.
• Calculate the area of a triangle using ½ab sin C, with C the angle included between sides a and b.
• Explain the ambiguous case of the sine rule, finding both possible angles (x and 180° − x) when both give a triangle.

You will be able to

• Recall the exact values of sin, cos and tan of 0°, 30°, 45°, 60° and 90°, and explain them from the 30°–60°–90° and 45°–45°–90° triangles.
• Sketch and describe the graphs of y = sin x, y = cos x and y = tan x for 0° ≤ x ≤ 360°, including their period, amplitude and the asymptotes of tan x.
• Solve sin x = k, cos x = k and tan x = k for 0° ≤ x ≤ 360°, using the principal value and the symmetry of the graph for the second solution.

You will be able to

• Calculate the length of a space diagonal of a cuboid and a slant edge of a pyramid by using Pythagoras' theorem in two right-angled triangles.
• Identify the projection of a line on a plane and calculate the angle between the line and the plane.
• Explain why the angle with the base is measured to the projection, not to a vertical edge or a base edge.