All About Trigonometric Ratios
Trigonometric ratios are pretty cool mathematical functions that connect the angles and sides in right-angled triangles. Let's dive into the basics of trigonometry, explore the six key ratios, and learn how to find them like a pro!
What are Trigonometric Ratios?
Trigonometric ratios are ratios that connect an angle of a right triangle to the ratio of two sides. They come in handy when studying geometry and geometry-related sciences. Real-life applications range from astronomy and aviation to musical production. There are six trigonometric ratios you need to know, then you’re all set!
What are the 6 Trigonometric Ratios?
How are the six fundamental trigonometric ratios for any triangle ABC defined? Let’s consider the angle C.
"Opposite" refers to the side length the angle faces, "adjacent" refers to the side length next to the angle, and "hypotenuse" refers to the longest side length, opposite to the right angle.
Here’s a tip use SOH-CAH-TOA to easily remember your trigonometric ratios!
SOH: Sine is Opposite over Hypotenuse
CAH: Cosine is Adjacent over Hypotenuse
TOA: Tangent is Opposite over Adjacent
The last three ratios are considered reciprocal trigonometric functions as they are the multiplicative inverse of the first three ratios.
How do you find trigonometric ratios?
Let’s now see how to find trigonometric ratios for a given triangle! It may seem scary, but trust me, it’s really simple once you get the hang of it. All you need to know is the length of the sides.
Let's consider a right-angled triangle.
We can see that for angle C, the lengths of the triangle's sides are as follows:
Opposite side (AB): 3 units
Adjacent side (BC): 4 units
Hypotenuse (AC): 5 units
With this information, finding the ratios will be a piece of cake! Remember SOH-CAH-TOA!
sin(C) = Opposite/Hypotenuse = 3/5
cos(C) = Adjacent/Hypotenuse = 4/5
tan(C) = Opposite/Adjacent = 3/4
The remaining three ratios are the reciprocals of the first three:
cosec(C) = 1/sin(C) = Hypotenuse/Opposite = 5/3
sec(C) = 1/cos(C) = Hypotenuse/Adjacent = 5/4
cot(C) = 1/tan(C) = Adjacent/Opposite = 4/3
Awesome, we have successfully calculated the trigonometric ratios for angle C!
Final Thoughts on Trigonometric Ratios
With this knowledge, you are well-equipped to explore the intriguing world of trigonometry! Remember, practice is essential to mastering trigonometric ratios. Try applying these ratios to real-life problems to enhance your understanding. If you face difficulties, don't hesitate to seek assistance. UPchieve coaches are always here to guide you, just sign up for a free tutoring session and give it a go.