Trigonometry
What is Trigonometry:
Triangles are made of 3 angles connected by 3 segments. Triangles with the same degree of angles are called similar triangles, who have the same shape. Thus, with the fixed degree of angles in a triangle, the ratio of the length of each segment in the triangle is also fixed. With this, trigonometry studies the relationships between the angles and sides of triangles.
Trigonometric Ratios:
In right triangle ABC, ∠𝐵 is the right angle. Let segment a be the opposite side to ∠𝐴, segment c be the opposite side to ∠𝐶, and segment b be the opposite side to ∠𝐵 and the hypotenuse side of the triangle.
Special Angles:
When using trigonometry to solve math problems, there are some special angles and their corresponding trigonometry ratios that are often used. You can save a lot of time and work by remembering them.
Example Question:
In a right triangle △𝐴𝐵𝐶 with ∠B=90, side 𝐴𝐵=3 and side 𝐵𝐶=4. Calculate the values of s𝑖𝑛𝐴,𝑐𝑜𝑠𝐴,and 𝑡𝑎𝑛𝐴.
Solution:
Pythagorean Theorem：𝐴𝐶=√𝐴𝐵2+𝐵𝐶2. Thus, 𝐴𝐶=√32+42=√25=5.
Apply trigonometric ratios:
