Calculate cos, sin, tan
CONCEPTS
Triangle Properties
• Triangles are referenced by 3 letters. The triangle reference can start with any letter
(Ex: The triangle above can be referenced as Triangle…ABC, ACB, BAC, BCA, CBA, CAB, etc)
• The sides of triangles are typically referenced by lowercase letters (a, b, c) and corners are by uppercase letters (A, B, C)
Sum of Angles
• The sum of all angles in a triangle = 180° (angle A + angle B + angle C = 180°)
Right Triangle Properties
• Right triangles have one 90° angle, which is opposite of the hypotenuse
• A hypotenuse is only found in a right triangle
Ratio of Sides
• cos θ = adj / hyp = b/c
• sin θ = opp / hyp = a/c
• tan θ = opp / adj = a/b
• Acronym to remember formulas: sohcahtoa (sin opposite hypotenuse cos adjacent hypotenuse tan opposite adjacent)
• These properties are ratios, so the same equation can have multiple values (sin θ = 2/3 = 4/6 = 6/9)
PRACTICE PROBLEMS
Question 1 What is sin C (see picture below)?
-- Answer -- 3/5
sin C = opp / hyp = 3/5
Question 2 What is sin F (see picture below)?
-- Answer -- 9/15 or 3/5
sin C = opp / hyp = 9/15 = 3/5
Note these triangles are similar because the side lengths have the same proportions. Therefore, they have the same sin value. In other words, sin, cos, tan of an angle = value of proportion of 2 sides.
Question 3 For a triangle, sin θ = 3/5, cos θ = 4/5. What is tan θ?
-- Answer -- 3/4
sin = opp / hyp = 3/5, cos = adj / hyp = 4/5, so opp = 3 and adj = 4
tan = opp / adj = 3/4
ACT PRACTICE PROBLEMS
