Introduction to Trigonometry: common misconceptions

If your child says… “A bigger triangle has a bigger sine.”

Ask together

What happens to a fraction when its top and bottom both double?

What’s true

Matching angles give matching ratios because corresponding sides grow by the same factor.

If your child says… “The bottom number always gives the hypotenuse.”

Ask together

Which two sides did tangent compare before we calculated h?

What’s true

Tangent compares the two perpendicular sides, so its denominator describes the adjacent side.

If your child says… “Sine of 30° is larger than sine of 60°.”

Ask together

Which angle faces the shorter side in the right half of the equilateral triangle?

What’s true

In this triangle, the side facing 30° is shorter than the side facing 60°.

If your child says… “The angle is one-half.”

Ask together

Does one-half appear under Angle or Cosine in the table?

What’s true

One-half compares lengths; the angle is measured in degrees.

If your child says… “I can split sine across the plus sign.”

Ask together

Do the combined angle’s sine and the two added sines give matching values?

What’s true

Sine names a ratio for the whole angle inside its brackets.

If your child says… “Sine plus cosine always equals 1.”

Ask together

Did dividing Pythagoras remove the squares from the side ratios?

What’s true

The squares matter, and each identity requires every ratio in it to be defined.

If your child says… “Squaring a sum just squares each part.”

Ask together

When identical sum brackets multiply, what happens to their two cross-products?

What’s true

Squaring a sum also includes twice the product of its parts.