Find cos x if sin x cot x = 4.
I got 4 but isnt it impossible for cos to equal 4? Isnt it only supposed to range from -1 to 1?
the answer choices are
1)4
2)2
3)1
4)sqrt 2
You're quite right!
None of the answers can be correct, since they all exceed 1.
Could you check the question?
Thanks for answering! and yes i think there is an error in the question
In fact, (3) is a feasible answer, but does not suit the given question.
You are correct, the cosine function ranges from -1 to 1. So it is indeed impossible for the value of cosine to be equal to 4. There might be an error or ambiguity in the question or the provided answer choices.
However, let's solve the given equation sin(x) cot(x) = 4 and find the possible values of x.
To start, we'll rewrite cot(x) as 1/tan(x) since cotangent is the reciprocal of tangent.
sin(x) cot(x) = 4
sin(x) (1/tan(x)) = 4
Now, simplify by multiplying both sides of the equation by tan(x):
sin(x) = 4tan(x)
Substituting the identity sin(x) = opposite/hypotenuse and tan(x) = opposite/adjacent, we can relate these trigonometric functions to a right triangle with angles x:
opposite/hypotenuse = 4 * opposite/adjacent
Simplifying this equation further:
hypotenuse/adjacent = 1/4
Now, let's consider a right triangle with angle x. If the opposite side has a length of 1, then the adjacent side has a length of 4.
Using the Pythagorean theorem, we can calculate the hypotenuse:
hypotenuse² = opposite² + adjacent²
hypotenuse² = 1² + 4²
hypotenuse² = 1 + 16
hypotenuse² = 17
hypotenuse = sqrt(17)
Therefore, the possible values for cos(x) would be adjacent/hypotenuse:
cos(x) = 4/hypotenuse
cos(x) = 4/sqrt(17)
Hence, the correct answer choice would be 4/sqrt(17) if we assume there was an error with the given answer choices, as cosine cannot be 4.