A sine and a cosine are equal when their angles add to 90° — sin 40° and cos 50° are the same number. These free printable worksheets give one and ask for the other's angle, using the cofunction rule sin θ = cos(90 − θ).
The rule comes straight from a right triangle: the two acute angles add to 90°, and the side that is opposite one is adjacent to the other, so the sine of one is the cosine of its complement. A question gives sin 40° = cos ? and the answer is 50° — a whole number of degrees, the complement.
Why this sheet works
It is a no-calculator fact, so the page prints and the answer stays exact. The step-by-step walk names the cofunction rule and then subtracts from 90°, because the understanding to build is why the two are equal, not the subtraction itself.
How this one works
One question from this sheet, worked through a step at a time.
Complete sin 35° = cos ▢
sin θ=cos(90° − θ)
sin 35° = cos55°
A sine and a cosine are equal when their angles add to 90° — that is the cofunction rule.
Use the cofunction rule: sin θ = cos(90° − θ). Answer in degrees.
1sin 35° = cos
2cos 85° = sin
3cos 30° = sin
4cos 35° = sin
5cos 70° = sin
6cos 40° = sin
7cos 5° = sin
8sin 30° = cos
9cos 15° = sin
10sin 75° = cos
Trigonometric identities · Use complementary-angle cofunctionsAnswer key
1. sin 35° = cos 55°2. cos 85° = sin 5°3. cos 30° = sin 60°4. cos 35° = sin 55°5. cos 70° = sin 20°6. cos 40° = sin 50°7. cos 5° = sin 85°8. sin 30° = cos 60°9. cos 15° = sin 75°10. sin 75° = cos 15°
