How to find the values of the trigonometric functions of theta from the information given cot theta=1/4, sun theta<0?

gibbokf5

gibbokf5

Answered question

2022-12-26

How to find the values of the trigonometric functions of θ from the information given cotθ=14,sinθ<0?

Answer & Explanation

Collin Johns

Collin Johns

Beginner2022-12-27Added 10 answers

Step 1. To determine the values of the trigonometric functions of θ.
Consider the given information cotθ=14,sinθ<0.
To start with,
tanθ=1cotθ=114=4
The issue states that sine is negative, and as we can see from the example above, tangent is also negative.
Step 2: Apply the C-A-S-T sign rule:
Using the C-A-S-T sign rule, we determine that θ is in Quadrant 3.
We know that,
tanθ=oppositeadjacent,
So,
The opposite side measures is -4 units and the adjacent side measures is -1 unit (As a result of x,y=-,- in quadrant 3).
The hypotenuse is located using the Pythagorean Theorem:
(4)2+(1)2=h216+1=h2h=±17
However, the hypotenuse can never be negative. So 17.
All four of the remaining ratios can now be calculated as:
sinθ=oppositehypotenuse=-417
And,
cosecθ=1sinθ=hypotenuseopposite=-174
And,
cosθ=adjacenthypotenuse=-117
And,
secθ=1cosθ=hypotenuseadjacent=-17
Therefore, the values of the trigonometric functions of θ from the information given cotθ=14,sinθ<0 are calculated above.

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