Question

I'm not good at this so if anyone would mind helping I would really appreciate it.

1. Find sin x and csc y

2. Find tan x and cot y

3. Find cos x and sec y.

Answer 1

Step 1: Use the Pythagorean Theorem to find the missing length: a² + b² = c²

`5^2+7^2=c^2\\25+49=c^2\\74=c^2\\√(74)=c`

from the perspective of X:

• opposite = 5
• adjacent = 7
• hypotenuse = √74

from the perspective of Y:

• opposite = 7
• adjacent = 5
• hypotenuse = √74

`sin\ x=(opposite)/(hypotenuse)=(5)/(√(74))=(5√(74))/(74)\\\\csc\ y=(hypotenuse)/(opposite)=(√(74))/(7)\\\\tan\ x=(opposite)/(adjacent)=(5)/(7)\\\\cot\ y=(adjacent)/(opposite)=(5)/(7)\\\\cos\ x=(adjacent)/(hypotenuse)=(7)/(√(74))=(7√(74))/(74)\\\\sec\ y=(hypotenuse)/(adjacent)=(√(74))/(5)`