Finding Angles and Exact Values: Inverse Trig and Special Cases

Finding Missing Angles

When you know two sides of a right-angled triangle and need to find an angle, you use inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹ (also written as arcsin, arccos, arctan).

• If you know opposite and hypotenuse → θ = sin⁻¹(opp/hyp)
• If you know adjacent and hypotenuse → θ = cos⁻¹(adj/hyp)
• If you know opposite and adjacent → θ = tan⁻¹(opp/adj)

Using Your Calculator Correctly

Make sure your calculator is in degree mode, not radian mode. Enter the ratio first, then apply the inverse function. Round angles to one decimal place unless the question specifies otherwise.

Exact Values at Special Angles

For 30°, 45°, and 60°, you are expected to know exact values without a calculator:

• sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3
• sin 45° = √2/2, cos 45° = √2/2, tan 45° = 1
• sin 60° = √3/2, cos 60° = ½, tan 60° = √3

These values may appear in non-calculator sections of MYP assessments or in Criterion A knowledge tasks.

Applied Problems

At MYP Year 5 level, angle-finding questions often involve real contexts: the angle of a ramp, the bearing of a path, or the inclination of a roof. Practice translating the written description into a correctly labelled diagram before writing any equations.

Common Mistakes

• Calculator left in radian mode, producing completely wrong angle values
• Confusing sin⁻¹(x) with 1/sin(x) — they are not the same
• Misidentifying which sides are given and selecting the wrong inverse function