Integrated Math 2 / Unit 7: Right Triangle Trigonometry
7.3 Sine, Cosine and Tangent
Notes
For an acute angle $A$ in a right triangle (SOH CAH TOA):
- $\displaystyle \sin A = \frac{\text{opposite}}{\text{hypotenuse}}$
- $\displaystyle \cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$
- $\displaystyle \tan A = \frac{\text{opposite}}{\text{adjacent}}$
- Opposite and adjacent depend on which angle you use. The hypotenuse never changes.
- Cofunction facts: $\sin A = \cos(90° - A)$, so $\sin 25° = \cos 65°$.
Practice
In a right triangle with legs 8 and 15 and hypotenuse 17, what is $\tan A$ for the angle $A$ opposite the side of length 8?
$\displaystyle \tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{15}$.
In a right triangle with legs 8 and 15 and hypotenuse 17, what is $\cos A$ for the angle $A$ opposite the side of length 8?
The side adjacent to $A$ is 15, so $\displaystyle \cos A = \frac{15}{17}$.
Which expression equals $\sin 25°$?
Sine of an angle equals cosine of its complement: $90° - 25° = 65°$.
Ready for more? Take the Unit 7 test.