Standard +0.3 This is a standard reciprocal trig equation that uses the identity sec²θ = 1 + tan²θ to convert to a quadratic in sec θ, then solve and find angles. It's slightly above routine due to the algebraic manipulation required, but follows a well-established method with no novel insight needed.
Attempt solution of 3-term quadratic equation to find one value of \(\theta\), from \(\cos\theta = \ldots\)
M1
Obtain \(73.4\)
A1
or greater accuracy
Obtain \(286.6\)
A1
or greater accuracy; and no others between 0 and 360
5
**Question 1:**
| Answer | Mark | Guidance |
|--------|------|----------|
| Attempt to express equation in terms of $\sec\theta$ only | M1 | or equivalent in terms of $\cos\theta$ only, using a correct identity, allow if '5' omitted |
| Obtain $6\sec^2\theta - 17\sec\theta - 14 (= 0)$ | A1 | or $14\cos^2\theta + 17\cos\theta - 6 = 0$ |
| Attempt solution of 3-term quadratic equation to find one value of $\theta$, from $\cos\theta = \ldots$ | M1 | |
| Obtain $73.4$ | A1 | or greater accuracy |
| Obtain $286.6$ | A1 | or greater accuracy; and no others between 0 and 360 |
| | **5** | |