1. sin x = cos y...what is (x+y)?

Question

2. cot 410 degrees=
A. -tan 50 degrees
B. tan 50 degrees
C. cot 310 degrees
D. tan 310 degrees
E. cot 50 degrees

please explain if possible. and if you know the fundamentals of pre calculus please let me know because i need to study for a test and i vaguely remember anything from pre-calculus.
thank you. any help will be greatly appreciated.

Answer 1

1. This is always true if x and y are complements, so x+y = 90°. There can be other instances for x and y (like sin 150° = cos 60°), but you can say for sure it's always true when x+y = 90.

2. 410° - 360° = 50°, so 410° is coterminal with 50°. That means it terminates in the same position and therefore has all the same trig ratios. So cot 410° = cot 50° [E]

Answer 2

1. x+y could be 90. Think of a right triangle. There are 3 angles, 90, x, and y. sin(x) is the ratio of the side opposite angle x to the hypotenuse (long side), and cos(y) is the ratio of the side next to angle y to the hypotenuse.

But the side opposite x is the side next to y, so it must be the same ratio!

90 is not the only possible answer, but it's probably the one they're looking for.

2. All trig functions repeat every 360 degrees. So cot(410) = cot(410-360).

tan and cot actually repeat twice every 360 degrees (once every 180) but it's better to just remember 360 because that also applies to sin, cos, sec, csc...

Answer 3

sin x = cos y...what is (x+y)?
x = y = 45 degrees
So x + y = 90 degrees

Since this is not one of the given answers, I feel you have left something out of the question.

Answer 4

90 degrees.