Standard +0.3 This is a standard C3 trigonometric equation requiring the Pythagorean identity sec²θ = 1 + tan²θ to convert to a quadratic in tan θ, then solving and finding angles in the given range. Slightly above average difficulty due to the use of sec/tan rather than sin/cos, but follows a well-practiced procedure with no novel insight required.
Attempt use of identity linking \(\sec^2\theta\), \(\tan^2\theta\) and 1
M1
To write eqn in terms of \(\tan\theta\)
Obtain \(\tan^2\theta - 4\tan\theta + 3 = 0\)
A1
Or correct unsimplified equiv
Attempt solution of quadratic eqn to find two values of \(\tan\theta\)
M1
Any 3 term quadratic eqn in \(\tan\theta\)
Obtain at least two correct answers
A1
After correct solution of eqn
Obtain all four of 45, 225, 71.6, 251.6
A1
5 Allow greater accuracy or angles to nearest degree – and no other answers between 0 and 360
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt use of identity linking $\sec^2\theta$, $\tan^2\theta$ and 1 | M1 | To write eqn in terms of $\tan\theta$ |
| Obtain $\tan^2\theta - 4\tan\theta + 3 = 0$ | A1 | Or correct unsimplified equiv |
| Attempt solution of quadratic eqn to find two values of $\tan\theta$ | M1 | Any 3 term quadratic eqn in $\tan\theta$ |
| Obtain at least two correct answers | A1 | After correct solution of eqn |
| Obtain all four of 45, 225, 71.6, 251.6 | A1 | **5** Allow greater accuracy or angles to nearest degree – and no other answers between 0 and 360 |
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