Sine and Cosine of Complementary Angles
Aligned to G-SRT.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
In a right triangle, the two acute angles are complementary (they add to 90°). The side opposite one acute angle is adjacent to the other, so the sine of one angle equals the cosine of its complement: sin t = cos(90 - t).
Worked example
Show sin 30° = cos 60°. In a right triangle, if one acute angle is 30°, the other is 90 - 30 = 60°. The leg opposite the 30° angle is the leg adjacent to the 60° angle. So sin 30° (opposite/hyp for 30°) equals cos 60° (adjacent/hyp for 60°). Both equal 0.5.
Practice questions
- Rewrite sin 25° as a cosine of a complementary angle.
- If cos 40° = 0.766, what is sin 50°?
- Explain why sin t always equals cos(90 - t) in a right triangle, using the words opposite and adjacent.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Seno y coseno de ángulos complementarios
En un triángulo rectángulo, los dos ángulos agudos son complementarios (suman 90°). El lado opuesto a un ángulo agudo es adyacente al otro, así que el seno de un ángulo es igual al coseno de su complemento: sen t = cos(90 - t).
Ejemplo: Muestra que sen 30° = cos 60°. En un triángulo rectángulo, si un ángulo agudo es 30°, el otro es 90 - 30 = 60°. El cateto opuesto al ángulo de 30° es el cateto adyacente al ángulo de 60°. Así, sen 30° (opuesto/hip para 30°) es igual a cos 60° (adyacente/hip para 60°). Ambos valen 0.5.
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