Trigonometry / Unit 2: Right Triangle Trigonometry
2.6 Cofunctions and Complementary Angles
Notes
In a right triangle the two acute angles are complementary, so the sine of one equals the cosine of the other.
- $\sin\theta = \cos(90^\circ - \theta)$, $\tan\theta = \cot(90^\circ - \theta)$, $\sec\theta = \csc(90^\circ - \theta)$.
- Example: $\sin 25^\circ = \cos 65^\circ$.
- To solve $\sin A = \cos B$ for acute angles, set $A + B = 90^\circ$.
Practice
Which expression equals $\sin 20^\circ$?
$\sin\theta = \cos(90^\circ - \theta)$.
For acute angles, $\sin x = \cos(2x + 6^\circ)$. What is $x$?
$x + (2x + 6^\circ) = 90^\circ$, so $3x = 84^\circ$ and $x = 28^\circ$.
Given $\sin 50^\circ \approx 0.766$, what is $\cos 40^\circ$ approximately?
$\cos 40^\circ = \sin(90^\circ - 40^\circ) = \sin 50^\circ$.
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