4 self-marking Additional Maths practice questions on The six trig functions for any magnitude, written specifically for Cambridge IGCSE Additional Maths (0606) across Single tier. Instant marking with full worked solutions on every question.
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Question 13 marksGrade 7
An equilateral triangle has side length 2 units. It is bisected by a line from one vertex to the midpoint of the opposite side, forming two congruent right-angled triangles.
Use this construction to find the exact value of sin60∘. [3]
Show the worked solution
Bisecting the equilateral triangle gives a right-angled triangle with hypotenuse 2
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Assumes all trigonometric functions share the same sign in a given quadrant, not recognising that a ratio of two negative values (e.g. tan) is positive
200∘ lies in the third quadrant (180∘ to 270∘
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(a side of the original triangle), base
1
(half the bisected side), and a
60∘
angle at the original vertex.
By Pythagoras, the height =22−12=3.
sin60∘=hypotenuseopposite=23.
Question 23 marksGrade 8
State whether each of sin200∘, cos200∘, and tan200∘ is positive or negative. [3]
Show the worked solution
200∘ lies between 180∘ and 270∘, the third quadrant.
In the third quadrant: sin
Question 33 marksGrade 8
θ is an acute angle such that tanθ=125.
Find the exact value of cosecθ. [3]
Question 42 marksGrade 9
θ is an angle in the third quadrant such that sinθ=−53.
Find the exact value of tanθ. [2]
), where sin and cos are both negative - but tan, being their ratio, is the ratio of two negatives, which is POSITIVE.
Confuses one trigonometric reciprocal ratio with another, giving the wrong side ratio for the ratio requested
cosecθ is the reciprocal of sinθ, not related directly to tanθ - using the triangle with opposite 5, adjacent 12, hypotenuse 13, sinθ=135, so cosecθ=513.
Keeps a trigonometric ratio's sign as positive (or otherwise wrong) instead of applying the correct sign convention for the given quadrant
In the third quadrant, BOTH sinθ and cosθ are negative, not just sinθ - so cosθ=−54, making tanθ=−4/5−3/5=43, a POSITIVE value (tan is positive in the third quadrant).