Question

Which of the following statements are true regarding triangle ABC? (Just type the letters in the box)

a) sin(a) = sin()
b) csc(a) = 5/3
c) tan(a) = tan(c)
d) sin(a) = cos(c)
e) cos(c) = sin(a)
f) tan(a) =
g) cos(a) = 3/5
h) csc(a) = 5/3

Answer 1

The true statements regarding triangle ABC are sin(a) = sin(β), tan(a) = tan(c), and cos(a) = 3/5.

Step-by-step explanation:

From the given statements, we can determine that the correct options are:

• a) sin(a) = sin(β)
• c) tan(a) = tan(c)
• g) cos(a) = 3/5

Let's explain why:

1. a) sin(a) = sin(β): This is a true statement since sine is a periodic function, meaning sin(x) = sin(x + 2π) for any value of x. Therefore, sin(a) = sin(β).
2. c) tan(a) = tan(c): This is also a true statement since tangent is another periodic function, tan(x) = tan(x + π) for any value of x. Hence, tan(a) = tan(c).
3. g) cos(a) = 3/5: This statement is true only if the angle a is associated with a specific triangle. However, without any information about the triangle, we cannot verify if this statement is true or not.