How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=9, b=40, c=41?

Answer 1

See below:

Given that this is a right triangle, let's put side a along the positive #x# axis, side b along the #y# axis, and side c is the hypotenuse.

Now the question is Which angle are we concerned with? Is it angle A? Angle B? Or even the right angle, angle C?

Since we aren't given which angle, I'll work all 3.

The 6 trig functions are #sin, cos, tan, csc = 1/sin, sec = 1/cos, cot = 1/tan# (maybe you've learned SOHCAHTOA, or #Sin = "Opp"/"Hyp", Cos = "Adj"/"Hyp", Tan = "Opp"/"Adj"#).

Angle A

Angle A has as its opposite side a, which means it's two sides are 1. along the #y# axis and 2. the hypotenuse:
#sin=9/41; csc = 41/9#
#cos = 40/41; sec = 41/40#
#tan = 9/40; cot = 40/9#

Angle B

Angle B has as its opposite side b, which means it's two sides are 1. along the #x# axis and 2. the hypotenuse:
#sin=40/41; csc = 40/41#
#cos = 9/41; sec = 41/9#
#tan = 40/9; cot = 9/40#

Angle C

Angle C is the right angle:

#sin=1; csc = 1#
#cos = 0; sec = "undefined"#
#tan = "undefined"; cot = 0#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7