- Write `8 cos x + 6 sin x` in the form `A cos(x −α)`, where `A > 0` and `0 ≤α ≤ π/2`. (2 marks)
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- Hence, or otherwise, solve the equation `8cos x + 6 sin x = 5` for `0 ≤ x ≤ 2π`.
Give your answers correct to three decimal places. (2 marks)
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Trigonometry, EXT1 T3 2015 HSC 11d
Express `5 cos x - 12 sin x` in the form `A cos (x + α)`, where `0 ≤ α ≤ pi/2`. (2 marks)
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Trigonometry, EXT1 T3 2014 HSC 2 MC
Which expression is equal to `cos x - sin x`?
(A) `sqrt 2 cos (x + pi/4)`
(B) `sqrt 2 cos (x - pi/4)`
(C) `2 cos (x + pi/4)`
(D) `2 cos (x - pi/4)`
Trigonometry, EXT1 T3 2013 HSC 12a
- Write `sqrt3cos x - sin x` in the form `2 cos (x + alpha)`, where `0 < alpha < pi/2`. (1 mark)
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- Hence, or otherwise, solve `sqrt3 cos x = 1 + sin x`, where `0 < x < 2pi`. (2 marks)
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Trigonometry, EXT1 T3 2010 HSC 4b
- Express `2 cos theta + 2 cos (theta + pi/3)` in the form `R cos (theta + alpha)`,
where `R > 0` and `0 < alpha < pi/2`. (3 marks)
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- Hence, or otherwise, solve `2 cos theta + 2 cos (theta + pi/3) = 3`,
- for `0 < theta < 2pi`. (2 marks)
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