CAIE A-Level Mathematics 2.3.1 Reciprocal Trigonometric Functions

Practise converting sec, cosec and cot to cosine, sine and tangent, applying reciprocal identities and selecting all valid solutions over positive or negative angle ranges.

Exam points

replace sec θ, cosec θ or cot θ by its reciprocal or sine–cosine ratio
use identities such as cosec² θ = 1 + cot² θ to form a solvable quadratic
convert valid reciprocal values back to trig ratios and find every angle in the interval

[Maximum number: 2]

It is given that $3 \sin 2 \theta=\cos \theta$ where $\theta$ is an angle such that $0^{\circ}<\theta<90^{\circ}$ .

Find the exact value of $\sec \theta$ .

Use correct identity or identities to find value of $\sec \theta$
M1
Obtain $\frac{6}{\sqrt{35}}$ or exact equivalent
A1

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2.3.1—Reciprocal trig functions question 1