#21
Top 50 Mistake
Not using inverse functions to find angles
"The Inverse Forget"
The Mistake in Action
In a triangle, Opposite = 6cm and Hypotenuse = 10cm. Find the angle.
Wrong: $\sin(\theta) = \frac{6}{10} = 0.6$ $\theta = 0.6°$
Why It Happens
Students correctly find sin(θ) = 0.6 but then think that IS the angle. They don't realise they need to use the inverse sine function to find θ.
The Fix
0.6 is not the angle — it's the VALUE of sin(θ).
To find the angle, use inverse sine (sin⁻¹ or arcsin):
$$\theta = \sin^{-1}(0.6) = 36.9°$$
On your calculator: Press SHIFT then SIN, then enter 0.6.
Spot the Mistake
Can you identify where this student went wrong?
Opposite = 6cm, Hypotenuse = 10cm. Find angle θ.
$\sin(\theta) = \frac{6}{10} = 0.6$
$\theta = 0.6°$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: