Learn the six trigonometric ratios (sin, cos, tan, and their reciprocals) in a right triangle, and evaluate expressions involving them.
In a right triangle, sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse, tanθ=opposite/adjacent. Their reciprocals are cosecθ, secθ, and cotθ.
In a right triangle, opposite=3, adjacent=4, hypotenuse=5. Find sinθ and cosθ.
sinθ=3/5, cosθ=4/5
If tanθ=3/4, find secθ.
Using a 3-4-5 triangle, hypotenuse=5; secθ=hypotenuse/adjacent=5/4
In a right triangle, opposite=8, adjacent=15, hypotenuse=17. Find sinθ and tanθ.
sinθ=8/17, tanθ=8/15
Using the fundamental identity sin²θ+cos²θ=1, trigonometric expressions can be simplified or evaluated.
If sinθ=5/13, find cosθ using the identity.
cos²θ=1−25/169=144/169; cosθ=12/13
Evaluate: sin²30°+cos²30°
By the identity, this always equals 1
If cosθ=7/25, find sinθ using the identity.
sin²θ=1−49/625=576/625; sinθ=24/25
1. In a right triangle, opposite=5, adjacent=12, hypotenuse=13. Find sinθ and tanθ.
2. If cosθ=8/17, find sinθ using the identity.
3. If sinθ=1/2, find cosecθ.
4. Evaluate: sin²45°+cos²45°
5. If tanθ=1, find θ.
6. In a right triangle, opposite=9, adjacent=40, hypotenuse=41. Find sinθ and cosθ.
7. If sinθ=8/17, find cosθ using the identity.
8. If cosθ=3/5, find secθ.
9. Evaluate: sin²60°+cos²60°
10. If tanθ=√3, find θ.