Foundation June 2022 Paper 3 Q21
21 Use trigonometry to work out the size of angle \(x\). [3 marks]
Not drawn accurately
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| tan identified | M1 | oe eg \(\tan^{-1}\) |
| \(\tan x = \dfrac{10}{4}\) or \(\tan x = \dfrac{5}{2}\) or \(\tan x = 2.5\) | M1dep | oe eg \(\tan^{-1} \dfrac{10}{4}\) or \(90 - \tan^{-1} \dfrac{4}{10}\) |
| [68, 68.2] | A1 | SC1 [21.8, 22] |
| Alternative method 2 | ||
| \(\sin x = \dfrac{10}{\sqrt{4^2 + 10^2}}\) or \(\cos x = \dfrac{4}{\sqrt{4^2 + 10^2}}\) | M2 | oe eg \(\sin x = \dfrac{10}{\sqrt{116}}\) or \(\sin^{-1} \dfrac{10}{\sqrt{4^2 + 10^2}}\) or \(\cos x = \dfrac{4}{\sqrt{116}}\) or \(\cos^{-1} \dfrac{4}{\sqrt{4^2 + 10^2}}\) or \(90 - \sin^{-1} \dfrac{4}{\sqrt{4^2 + 10^2}}\) or \(90 - \cos^{-1} \dfrac{10}{\sqrt{4^2 + 10^2}}\) |
| [68, 68.2] | A1 | SC1 [21.8, 22] |
Additional guidance
| Accept 10.77 or 10.8 or \(2\sqrt{29}\) for \(\sqrt{116}\) | |
| Tan can be identified by, for example, circling TOA in SOHCAHTOA | |
| Answer from accurate drawing | M0M0A0 |
| \(\sin x = \dfrac{10 \sin 90}{\sqrt{116}}\) | M2 |
| \((x =)\) tan 2.5 or \((x =)\) tan 0.4 or \((x =)\) \(\tan \left(\dfrac{10}{4}\right)^{-1}\) unless recovered | M1M0A0 |
| \(\tan = \dfrac{10}{4}\) or \(\tan = \dfrac{4}{10}\) or \(\tan x = \dfrac{4}{10}\) with no further correct working | M1M0A0 |