CAIE IGCSE Additional Math 10.1 six trigonometric functions

Use this six-functions page to find exact trigonometric values, connect reciprocal functions and use diagram information to solve for unknowns.

Exam points

Find exact sine and cosine values from triangles or trigonometric relationships.
Use reciprocal trigonometric functions such as sec, cosec and cot where required.
Use exact trigonometric values to solve for unknown lengths or variables.

[Maximum number: 3]

Figure for Question 10.1. Use the six trigonometric functions question 1 — CAIE IGCSE Additional Math

The diagram shows an equilateral triangle ABC with side a.
M is the midpoint of AC and angle $AMB=90^\circ$ .
Use the diagram to find $\sec 30^\circ$ .

$\frac{2}{\sqrt{3}}$ or $\frac{2\sqrt{3}}{3}$
B2 for $[BM=]\frac{\sqrt{3}a}{2}$ or $\sec^2 30=1+\left(\frac{1}{\sqrt{3}}\right)^2$ or $\cos^2 30=1-\left(\frac{a/2}{a}\right)^2$ oe
B1 for $[BM^2=]a^2-\frac{a^2}{4}$ soi

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10.1. Use the six trigonometric functions question 1