3 mistakes learners make with trigonometry, each one named and explained.
Label the sides against the angle first. The labels choose the ratio.
The two sides are divided the wrong way round, so 7 over 24 becomes 24 over 7.
Both numbers are in the question and only the labels decide which goes on top.
Question. Opposite 7, adjacent 24
A common answer. tan inverse of 24/7
The answer. tan inverse of 7/24
Why. Tangent is opposite over adjacent, so the opposite side goes on top.
Sketch the triangle roughly to scale. The answer should look like the angle you drew.
The formula is divided where it should be multiplied, so the answer is a reciprocal too big or small.
The three quantities can be arranged three ways and only one of them is right for this unknown.
Question. Opposite wanted, hypotenuse 10, angle 30
A common answer. 10 / sin(30) = 20
The answer. 10 x sin(30) = 5
Why. The opposite side is shorter than the hypotenuse, so it cannot be 20.
A side found from the hypotenuse must be shorter than it. That check catches this every time.
Cosine is used where sine belongs, or tangent where cosine belongs.
All three ratios take an angle and give a number, so nothing about the calculation objects.
Question. Opposite side wanted, hypotenuse known, angle 30
A common answer. 10 x cos(30)
The answer. 10 x sin(30)
Why. Sine links the opposite to the hypotenuse, which is exactly the pair in the question.
Label the two sides in the question first. The pair of labels names the ratio.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.